But what you fail to realise is that he has the sixth most common given name in 1st century Palestine (according to the lecture), therefore everything in the Gospels must be true.
That seems like a completely watertight argument. I can't see a massive gaping hole in it anywhere /sarcasm.
I watched a bit of the video and he is a rather engaging speaker but his arguments are very weak.
He seems to fail to understand the difference between necessary and sufficient in term of the correct details in the gospels and they being based on eye witness accounts, let alone true.
Sure if the gospels were riddled with names and cultural/societal details that are demonstrably not consistent with 1stC palestine then we would easily dismiss they as being completely detached from eye witnesses. But that is only a necessary step, not a sufficient one to give credence to eye witnesses. Being able to include the right names and cultural details provides no positive evidence that the stories are based on eye witness accounts - the details might be correct, but the story completely made up as is often the case in fiction.
But even were the stories to be based on eye witness account, we know that untrained observers of events can be incredibly poor at recounting what actually happened, even if asked straight away. Add to that the 'lost in translation' of decades and the selection of narratives to suit a faith position rather than a historically accurate position and the accounts in the gospels are likely to be massively different to what actually happened, even if based on some original eye witness accounts.
And the final point is the implausibility - if the gospels made entirely plausible claims (e.g. Jesus died, the end), while we might still be uncertain of the eye witness veracity we may give the account the benefit of the doubt. But the gospels made implausible and extraordinary claims, and they require extraordinary evidence if we are to accept them. That evidence does not exist and is no stronger just because the gospels got the names of people right.