This would be a strange scenario because why would you keep these people employed? If someone doesn't want to do the job required, including servicing Postgres, then they wouldn't be with me any longer, I'll find someone who does.
And especially having worked in startups, I was expected to do many different things, from fixing infrastructure code one day to writing frontend code the next. If you're in a bigger company, maybe it's understandable to be specialized, but especially if you're at a company with only a few people, you must be willing to do the job, whatever it is.