I am as happy no where else and in no other society, and all my wishes end, where I hope my days will end, at Monticello. Too many scenes of happiness mingle themselves with all the recollections of my native woods and feilds, to suffer them to be supplanted in my affection by any other. - Thomas Jefferson from France to George Gilmer of Albemarle County, VA, 12 Aug 1787

Yes, the historic consensus overwhelmingly supports that Jefferson and Adams both died July 4th, 1826, as reported.

The account of Jefferson's death comes from numerous people, most notably his grandson Thomas Jefferson Randolph, his granddaughter's husband Nicholas Trist, and his attending doctor Robley Dunglison, all three later recording the event in writting. While their stories vary ever so slightly, they overwhelmingly tell the same timeline of Jefferson's decline and subsequent death at roughly 12:50 PM, 50 years to the day after his declaration to George III was signed by Congress. Martha, his daughter with whom he had always had a very close bond, was also dutifully by his side at the end as he struggled to last until the fourth. He had become bed ridden several days earlier and was slipping in and out of consciousness starting on the 2nd. He awoke briefly on the night of the third, and this is where stories get a smidge different. According to one account (Dunglison's), he questioned "Is it the fourth?", to which the doctor replied "It soon will be" before Jefferson slipped back to sleep. According to Trist, he asked "It is the fourth?" which Trist ignored until pressed a second time, not sure of what to say, at which point he lied and falsely acknowledged it was (which he later said he felt "repugnant" for doing). A third version comes from Randolph, who claimed Jefferson said definitively "It is the fourth of July." Monticello historians have a simple explanation for this discrepancy;

Actually, it would not be unreasonable to take each observer literally. One reconstruction of the event might take this shape: Jefferson wakes and utters his declaration, "This is the Fourth of July." Dunglison says, "It soon will be." Confused, Jefferson puts the question to Trist, "This is the Fourth?" He queries again and receives Trist's nodding assent. Then he sleeps until 9 p.m.

At 9 he awoke and was offered more Laudanum to which he replied "No, doctor, nothing more," which some believe to be his last words. They weren't. He woke again at about 4:00 AM and called his servants in with a clear voice, then spoke with them briefly - and that conversation has been lost to history. I like to believe his last words were similar to another slaveholder some years later who upon his death said "I hope and trust to see you all in heaven, both white and black," but we honestly just don't know what was said in those moments and whatever it was is the last thing he ever said.

At 12:50, 17 years after retiring from 40 years of public service to his neighbors, county, state, country, and fellow man, and surrounded by a gaggle of his grandchildren, Mr Jefferson passed away as the church bells of Charlottesville could be heard in the distance ringing in jubilation for our nation's 50th anniversary.

Self evident from this story is an overwhelming desire to make it to the fourth (sorry). Indeed, the 83 year old Jefferson had indicated as much and had often groaned of the difficulty in being so old and in so poor health, almost welcoming his death in some correspondence. Adams was in better health overall - but was also seven years older than Jefferson.

Adams was attended by his doctor Amos Holbrook and Abigail's neice/adopted daughter Louisa Smith around the clock, as well as random other family rotationally. He, too, had fallen quite ill and was awaiting the fourth. He had been seated in his library armchair, his favorite seat, on June 30th when Rev George Whitney and some others visited. Whitney knew his time was short for on the 27th of the same he had visited and later recorded of the visit "The old man fails fast." They had come this day, they said, to ask for a toast to be read on the fourth. Adams' reply was simple;

I will give you Independence forever!

When asked if he would like to add anymore to that his response was equally simple;

Not a word.

Holbrook had began to attend around the clock, and on the 1st Adams could barely talk. On the third a common visitor, John Marston, paid a visit but was unable to understand anything mumbled by the great statesman, later saying "...his countenance expressed all I could desire." On the fourth Whitney again visited and later wrote "the old gentleman was drawing to his end. Dr Holbrook was there and declared to us that he could not live more through the day." Adams soon awakened and was told it was the fourth, and he replied;

It is a great day. It is a good day.

About this time, Jefferson breathed his last and slipped away to reunite with 5 of his 6 (white) children and his beloved wife, all having been survived by him.

As the cannons sounded in Massachusetts, even God joined in with thunderous roars from the skies. Soon a light rain fell, and Adams again awoke. It is said by some he stated "Thomas Jefferson survives" (or a variation thereof), then lingered for a bit. According to McCullough in John Adams, he then whispered to his granddaughter Susanna "Help me, child! Help me!" and then fell silent. About 6:20 PM the second president passed away and rejoined so many family members he too had lost over the years. Later, Eliza Quincy, wife of the Mayor, would relay what he claimed to be told by Louisa following Adams' death;

the last words he distinctly spoke was the name 'Thomas Jefferson.' The rest of the sentence he uttered was so inarticulate, that she could not catch the meaning. This occurred at one o'clock - a few moments after Mr. Jefferson had died.

So that part may be a little fuzzy, but otherwise yes, they both died on the same day. Some have tried to attribute this to a number of factors; divine intervention, pure coincidence, mutual suicide, doctor assisted suicide/homicide, or just giving up on life having reached the finish line have all been suggested. And an argument can be made for any of them - Adams had written of the doctors familiarity with Hemlock and drugs of similar potency. Doctors surely over prescribed or administered medications, intentionally or not. And old men surely sought the end, either through medication or just lack of motivation to live, though there is not a trace to suggest either of these were a factor. We will never be able to say for certain but, to me at least, it seems perfectly clear: both men had a insatiable desire to see their creation turn 50, and imo they both would have died earlier without the motivator keeping them alive.