One of which outlines there is no parties, noise complaints, etc. 

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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.

File a complaint against them with the state licensing agency 

Criminal negligence, that's a thing.

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!

no complaint…

Unless they fixed it, apartments.com was having trouble with criminal background checks.

I cannot specifically think of any issue at all but occasionally we have had complaints about something clearly listed and when we point them to it the complaining usually stops. 

I checked the Better Business Bureau for complaints, I checked the NJ State Attorney General consumer division to ensure he was licensed, I checked every reference he gave by visiting sites and speaking with the homeowners.