I would be incrediably surprised if this were true. "Psychiatric Meds" covers an enourmous range of medications; stimulants, depressants, anti-depressants, antipsychotics/ neuroleptics, anti seizure, hallucinogens, anti anxiety, antimanic/ mood stabilizers, anti hypertensive...
The idea that somehow all of these medications shorten the lifespan by 15-20 years? Simply doesn't compute.
What I would be completely unsurprised to find, however, is a strong correlation between the population taking psychiatric medication & a shortened lifespan of apx 15-20 years. But that would be caused by dozens of attendant issues, very few of which are related to the medications themselves, and most of which related to things like; suicide, poverty, deit, weight, exercise, smoking, alcohol abuse, drug abuse, homelessness, inadequate healthcare, etc.
Correlation is not causation. There is a strong correlation of people inside of a catholic cathedral being catholic. But being inside the cathedral doesn't make one catholic.