So this is a statistic that has been called into question recently. The real number is likely somewhere between 0.3% and 0.7%, and this has been replicated a few times in various studies. Furthermore, in all of my reading, I can't actually find any justification for this 1% number. Most of the studies I've seen put estimates in the 0.3%-0.7% range (or even lower in some). It seems that there are a few outlier studies putting the number much higher (I saw 3% in one study, which in my opinion is definitely far too high) and this may drag up an average if it is not weighted. Again, though, I'm not sure why this 1% number continues to be repeated given the seemingly widespread scholarly work arguing for significantly lower estimates. The NIMH also puts the number in the 0.3%-0.7% range:
https://www.nimh.nih.gov/health/statistics/schizophrenia.shtml
Another thing about this that doesn't quite line up is the incidence estimates. Incidence estimates in scholarly articles tend to lie between 0.1/1000 and 0.7/1000 per year, this is 1-7 people in 10,000 people per year. Above, we are talking about lifetime prevalence, here we are talking about yearly incidence. They are not the same thing, but if the lifetime prevalence were indeed 1%, I would expect these yearly incidence rates to be a whole lot higher (0.7/1000 is very low). Source for the incidence rates:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2727721/
Anyway, I personally suspect it's probably closer to around 0.5%, approximately the same risk as developing a primary brain tumor. There are a lot of confounding factors here, and diagnosing schizophrenia is difficult for a variety of reasons. The international rates are further complicated by lack of access to appropriate healthcare in certain areas (do you think that people with schizophrenia living in, say, Syria are getting diagnosed? Probably not). Further complicating matters is the fact that schizophrenia often gets lumped in with all of the other psychotic-spectrum disorders in studies estimating incidence/prevalence, some of which are considerably different from schizophrenia itself. It's a difficult situation, but I do personally speculate that 1% is a bit high.