There being a smallpox epidemic in the Colonies during the Revolution doesn't really prove anything. While not as endemic in what would become the United States as it was in Europe, periodic epidemics were simply a fact of life.
That said, Fox is not entirely full of blarney, but is very much overstating its case. Washington did write the Continental Congress in late 1775, during his siege of Howe's troops in Boston, saying:
By recent information from Boston, Genl Howe is goeing to Send out a number of the Inhabitants in order it is thought to make more room for his expected reinforcements, there is one part of the information that I Can hardly give Credit to. A Sailor Says that a number of these Comeing out have been innoculated, with design of Spreading the Smallpox thro’ this Country & Camp. I have Communicated this to the General Court & recommended their attention thereto.
In other words, Washington is saying he thinks Howe is deliberately releasing people from besieged Boston who have been "innoculated." Notwithstanding the dubiousness of the source being an unnamed, but apparently highly informed, sailor, we need to understand what is meant by innoculation.
Better known today as "variolation" (to distinguish it from the more generic term), the practice was a very early form of acquiring immunity to smallpox through the deliberate exposure to scabs, pustules, pus, and other matter from infected persons. It originated in China where the practice was to snuff dried and powdered smallpox scabs. Throughout India, the Middle East/North Africa, and Sub-saharan Africa, the practice was to take a bit of pus from an infected person and introduce to a healthy person via a shallow cut in the skin, typically on the upper arm. This was the practice that (finally) made its way to Europe and the British American Colonies in the early 1700s, the latter being introduced in 1721 when Cotton Mather learned the technique from one of his slaves.
The practice may sound equal parts insane and suicidal but it has a sound biological basis and is in fact a very primitive form of attenuated virus vaccination. Smallpox can survive for a frighteningly long time in ideal circumstances, but samples will degrade if say, pus is taken from a infected person, put in a jar for a few days/weeks/months before being used to variolate someone. That person is basically getting a weakened virus, whose infection they will survive and gain lifelong immunity from. That's the general idea, anyway; there's no a lot of clinical studies being done on the pathogenesis of a virus that was eradicated more than 30 years ago using techniques that haven't been standard of care for 300 years.
The important fact here is that variolation can give you, basically, a mild case of smallpox. During that time, a variolated person may transmit their mild case of smallpox to a healthy person, who may then get a not-so-mild case of smallpox. Thus, variolation was typically accompanied with a period of isolation during which the person may experience everything from a mild fever to mild smallpox to actual now-you're-dead smallpox. Keep in mind this was a technique with wide variation on its actual deployment, and no real theoretical backing besides a general idea of contagion. Ideally, the variolated person would suffer relatively mild symptoms, at most a "local" smallpox infection at the inoculation site, and then have lifelong immunity thereafter. There's a classic early 19th Century series of drawings comparing variolation with the (then) brand new practice of vaccination that you can see here (taken from a largish PDF from the WHO on early smallpox control. You can see the how dramatic the difference is, with variolation producing a large, purulent wound within a ring of pustules, with more satellite pustules around the inoculated area.
Variolation, in other words, could indeed lead to a wider outbreak of smallpox if not managed correctly. As such, the practice was highly controversial in Colonial America, where smallpox was (as noted) less endemic than periodic. Better to take your chance on not getting the disease, or surviving it if you did, than to purposely infect yourself. Not getting variolated carried risks, but so did the procedure itself. Someone offering the practice could potentially be a danger. Fenn's (2001) Pox Americana: The Great Smallpox Epidemic of 1775-82, notes that Cotton Mather's house was actually firebombed because of his advocacy for variolation, with a friendly note that said, "COTTON MATHER, you dog, Dam you, I'l inoculate you with this, with a pox to you." Fenn also records several other cases of rioting to stop the practice and its banning by various levels of colonial government.
To return to 1775 Boston though, this is what Fenn has to say about the episode:
On November 24, 1775, General Howe granted permission for the residents of Boston to being their own variolations. Simultaneously, as Variola raced through the city, he began ordering selected citizens to leave. Whether the timing was deliberate is not known. Either way the result was the same: Washington now faced a flood tide of castaways who might well infect American lines.
Important to note here, however, is that the Bostonians' desire to variolate themselves was in response to a smallpox outbreak already present in the city. Note also that Fenn does not actually connect those who were ordered to leave, with those who were variolated, which would be the real proof of an intention to send possibly infectious people out to the American army. This sort of speculation is part and parcel for the possible practice of pox as a bio-weapon in the Revolutionary War. Even Jefferson has something to say on the matter, writing about "La Petit Varole" at the Battle of Quebec, he states:
I have been informed by officers who were on the spot, and whom I believe myself, that this disorder was sent into our army designedly by the commanding officer in Quebec. It answered his purpose effectually.
Jefferson was writing years after the fact, and was not actually in Quebec himself. Bioweapons expert Jonathan Tucker wrote in his 2002 book, Scourge: The Once and Future Threat of Smallpox, that the British commander, Gen Carleton, had (as in Boston) deliberately sent out inoculated persons from Quebec City to the American lines, but cites no source other than Jefferson. Becker (2004) states that Carleton may have "ordered or condoned sending contagious victims of the disease into the enemy lines," but perhaps overstates her case a bit, since the sole primary account that supports this is a 16 year old American soldier, John Joseph Henry, who wrote that:
the small pox, introduced into our cantonments by the indecorous, yet fascinating arts of the enemy, had already begun its ravages
Other accounts merely support the fact that a smallpox epidemic did occur among the American encampment.
The poor evidence for these situations invites speculation and finding one's own preferred interpretation in the evidence. Tucker, for example, cites Fenn as saying infected slaves who defected to the British were sent back to their plantations with the intention of causing further outbreaks. Fenn, however, says only that there were cases where infected slaves were turned away or abandoned by the British forces, rather than risk infection themselves or spare the supplies and effort to care for them. That's its own kind of inhumanity, but it is not a deliberate attempt at weaponizing smallpox patients.
I've said this before in various discussions about smallpox infections and intentionality with regards to European settlers and Native Americans, but it deserves reiterating: smallpox does not need much help in spreading. It was (is) one of the most infectious pathogens known to humanity and an 18th Century Army camp is pretty much an ideal scenario for its spread. Another soldier at Quebec, Caleb Haskell, presciently wrote:
The smallpox ... all around us, and there is great danger of it spreading in the army.
The evidence for these claims rest primarily on interpretations of primary sources without a lot of smoking guns and a great deal of extenuating circumstances. In the case with Boston and the slaves, a smallpox outbreak was already extant prior to any accusations of deliberate attempts to infect the Americans. In the case of both Quebec City and Boston, the sensible approach to an outbreak in the city would be to expel the infected from the city; whether or not that constitutes a deliberate attempt at bio-warfare depends on how you parse the very scant data.