It's worth remembering that it would have been just as easy to believe engines were near perfect when they were a few hundred points weaker. i.e. very weak.
Likewise world championship matches had a lot of draws when the players were about 800 points weaker than a top engine now. It did not mean they were perfect: it meant they were not good enough to obliterate the opponent almost 100% of the time.
The imminent draw death of chess has been an ongoing concern since Steinitz 
...every generation thinks they have exhausted chess and reached the pinnacle of understanding. Engines just extend this trend into waters human players will not even understand soon. I have already seen Carlsen say in an interview that he could not fathom a particular engine line in any way...it's only a matter of time before human players will cease to understand engine play even with perfect hindsight and seeing the eval numbers.
Requirements for a Poisson distribution (wiki):
“k is the number of times an event occurs in an interval and k can take values 0, 1, 2, ... .” -chess errors follow this.
...
Do they though?
An interval is described as a measured part of some infinitely divisible measurable space (time intervals, volumes etc.) with lim(p/δ) as δ→0 being a fixed value λ, where δ is the measure of an interval and p is the probability of an event occurring in the interval, from which a Poisson distribution as the limit of a binomial distribution can be inferred.
What is @tygxc assuming as that space?
He is apparently regarding the chess game as an interval of fixed measure (!), because he postulates a Poisson distribution for blunders per game, but what measurable space are those intervals meant to be embedded in? (And how does he then get to blunders per ply without knowing the game lengths? Is a ply also meant to be an interval and, if so, what would half a ply be?)
He doesn't say.
What Wiki is describing is actually the requirements for a Poisson process rather than a Poisson distribution. Maybe he's postulating a Poisson distribution for blunders per game without assuming a Poisson process, but he doesn't say why it should be plausible (and obviously it doesn't work),
thats true. calculations wise it comes down to almost the same thing, but you are right in that there is a distinction to be made.