He claims that Rome could no longer stand against it's barbarian enemies because many Romans were German at that point. Were there other factors in Rome's fall?
Not being snarky or anything, but there are a lot of related questions here in the wiki. The point you make is technically true. All citizens of the empire were given Roman citizenship with the Edict of Caracalla in 212. A lot of these people were Germanic, so in some ways it's true that the Romans were Germanic at that point. However the theory you talked about really isn't accepted anymore . That comes from Edward Gibbon's Decline and Fall of the Roman Empire which is highly influential but outdated at this point. Gibbon was writing that when Great Britain was an Empire, so there's a lot of biases in that work to take with a grain of salt.
As for why the WRE fell, the wiki can probably answer that better than I can. But to list off a few points, the Crisis of the Third Century, and the repeated encroachment of Germanic tribes across the Rhine were two big factors.
It's a common argument. It's considered the "classical" argument, and is not entirely out of vogue, as evidenced by Peter Heather's recent books "The Fall of the Roman Empire" and "Empires and Barbarians." However it's no longer the only argument, nor considered a monocausal argument.
The real problem lies in a few key words that need parsing within your question.
Understand that though it may seem pedantic/semantic to you, this parsing is actually very core to the last several hundred years of history and social science that has revolved around answering that most deceptively simple of questions, "Why did the Roman Empire end?"
Most academic debates about the end of the Western Roman Empire hinge on multiple causes, or qualified causes within a suggested primary cause (like migration). But you know, especially given recent thought on the literary nature of history, no one has a monopoly on "truth" or "plausibility" with regards to answering the "why" question, though you should be aware that there will be varying degrees of social acceptance as to different theories, dependent upon prevailing ways of thinking at that point in time.
But if you're interested in a tl;dr of the insanity involved with regards to the possible factors as to Rome's fall, check out this infamous list of 210 (frequently contradictory) reasons.
The answers you've got here, especially from /u/bitparity, are great. I'll add a quirky one. Bear with me. I promise this answers your question, kind of.
Edward Luttwak is a modern expert on contemporary military strategy, especially American capabilities. He's also a self-taught (amateur) classicist, but an impressive one at that. In 1976, he wrote a book called The Grand Strategy of the Roman Empire. It's very controversial among historians, but it's also a fascinating take on this very question.
The source of the controversy is that Luttwak is looking at Rome through a markedly American strategic lens. So while America might (does?) have a "grand strategy" for its self-defense and international goals, one arrived at by policy experts employing professional, technical analysis, Rome certainly did not. In the waning days of the Republic the Consuls for the year most certainly did not sit down with their Joint Chiefs of Staff to discuss grand policy for the next few decades. And if they did, that policy certainly was not transmitted to and adopted by the Caesars.
Roman military strategy was much more ad hoc -- when piracy was a problem, for example, the Senate voted Pompey an extraordinary command to eradicate it. Because he was in the area, he was then tapped to vanquish Rome's most recent foil, Mithridates of Pontus. Consuls and elite Romans pursued foreign policy goals for their own reasons, but adherence to a grand vision for Roman security was not one of them.
This is the problem with Luttwak's thesis. What is its merit? Well, Luttwak takes anecdote and piecemeal policy and argues that, whether or not they planned it, all of these actions DID add up to a coherent, national foreign policy. Rome's "Grand Strategy," he argues, was to guarantee the loyalty and security of reliable "buffer states" and client kingdoms. If any threat to Rome reared its head, it was met by the buffer states and a highly mobile Roman army together, making use of scattered front-line garrisons. In this manner Rome could ignore quiet borders but move quickly, with its allies, to meet the threat of anything that might have posed a systemic threat to the Empire itself, or its homeland.
Luttwak argues that this strategy ultimately failed for two reasons. First, Rome lost control of the buffer states, and pulled forces from the frontline garrisons. And second, but more importantly, while the buffer state system was adequate to the challenges Rome faced during the early Empire, it was inadequate to the challenge posed by a larger threat. Rome's veneer of invincibility was simply the product of the absence of a credible challenger. The Germanic migration was just too much for the system to bear.
I'm not representing this as true, it's just an interesting take to keep in mind, with the major caveat listed above.