It's not that the statistics are wrong, it's that you can't apply statistics to prove this at all. Specifically because the person you're analyzing knows all about chess. They know that a super strong weird move will just expose them, so instead they're going to pick lines that just slightly increase their strength. This is like the statistical analyses that show election rigging by highlighting a statistically improbable distribution of results - that analysis works if the person rigging the election doesn't consider the statistical analysis when they're doing their cheating, it is completely avoidable if you cheat competently.
Which brings us back to a sort of basic question - if this guy is cheating, do we think he's doing it fairly competently or not? If he's not cheating, the statistics will show normal play, if he is cheating and he's fairly competent the statistics will show normal play. So what has this analysis done? It's proved that he's not totally incompetent, which we already knew because he's pretty well established as a good chess player even he isn't truly a 2700ELO.
Which brings us back to a sort of basic question - if this guy is cheating, do we think he's doing it fairly competently or not? If he's not cheating, the statistics will show normal play, if he is cheating and he's fairly competent the statistics will show normal play. So what has this analysis done? It's proved that he's not totally incompetent, which we already knew because he's pretty well established as a good chess player even he isn't truly a 2700ELO.