As someone who is very much in favor of legalizing psychadelics and has enjoyed his experiences with them:
No, there is a lot of strong evidence that psychadelic trips can trigger underlying issues such as schizophrenia, etc.
However, some portion of these people would have it triggered these latent illnesses regardless of the use of these substances. The hard to answer question is how many people would develop these conditions without the drug use, if the drug use significantly accelerated it, etc.
On the subject of HPPD, I am more skeptical. It's very poorly understood, and there's been correlation shown for just about any sort of psychoactive substance, SSRIs, etc. Studies have claimed that anywhere from 5% to 25% of people who have taken recreational psychoactive drugs are impacted by it. Which, well, I have not done and am not qualified to do such a study, but having spoken to hundreds of users of psychadelic drugs over several decades and never encountering a single person who claimed to experience HPPD, it's hard to square up my anecdotal experiences with some of the reports.
Something is going on there - there's enough people that report the symptoms that I don't believe it's made up or anything like that - but it doesn't seem to be nearly as simply as "Anyone that does recreational drugs has a chance of developing HPPD"