If we model tennis points as random (let's say, accounting only for service), would we not expect people to occasionally lose when they had a match point? We'd expect this to happen more often when playing an opponent of comparable skill.
It's not obvious to me that it's psychological at all, and it seems to me that it's only reported as such because it makes a good news story.
According the most recent of these threads Federer's lose-after-match-point percentage is 1.4%. Djokovic's is 0.2%. Djokovic also has a much higher win-after-facing-match-point percentage. It's hard to claim that this is purely due to randomness.
If you want to convince yourself that choking is a thing, then this is a stat you might look at.
But, this stat is just as likely to be more influenced by how close your opponent's skill was on that day (how often you play opponents at a similar skill level), your and your opponent's relative stamina, whether those match points appeared in a regular service game or a tiebreak (how often your style of play goes to a tiebreak), and perhaps even pure luck - out of thousands of tour players, some are going to have incredible luck.
It's not obvious to me that it's psychological at all, and it seems to me that it's only reported as such because it makes a good news story.