That is where the concern would be for me.Yeah, older tenants may think that it automatically makes someone a criminal of something, but I would just explain the card and that it at least, in theory, has a medical purpose, unlike cigarette smoke which kills the smokers and everyone else around.

Think hard about your criminal background criteria.

If the applicant comes from the pool of people that I or my tenants know, I use real estate as a way to give back as many of my tenants will not qualify credit wise or may even have a criminal background or would struggle for another reason if I were to just stick to the "background/credit check" criteria. 

I'd venture to guess your tenant is a criminal or drug addict of some sort.There's some truth in your thought but he's actually a really nice hard working young man. 

Although, for it to be a criminal trespass.. something that will actually hold up, he would have to be present with the police there.

I mainly was curious about what legal grounds we have in order to proceed, since the PMA doesn’t specifically state “agent won’t grant criminals unsupervised access to your vacant property”, I figured that was just given!

Criminal background will weed out some bad actors as well.  

There are many scammers out there, with histories (criminal and financial) that they are not proud of, trying to raise money.

We are only allowed to screen non-tenant applicants for criminal and rental history, nothing financially related. 

However, if that effort fails, the local agent is equally liable – criminally and civilly – for any fees, fines, etc. associated with the property."