Well, I can kinda see where he's coming from. He did say 'Depending on the situation'. There are a lot of different types of mental illness out there. If you've got someone with an illness that can manifest itself in sudden violent outbursts, that's a legitimate safety concern. What if they fly into a rage and injure you, themselves, or another loved one?
Example: I had a friend whose ex-wife used to beat herself when she became upset. If he tried to get her to stop, she would turn and attack him. I've also received a few kicks/bites/scratches from trying to subdue her when somebody set her off at a party and she attacked them (Guy refused to defend himself and she would continue the assault when he tried to disengage/leave the party). She also suddenly jumped out of my truck at 20mph after agreeing to leave the party because she decided she wanted to go back and continue trying to kick the person's ass. All it would've taken was for her to grab a knife, gun, bat, etc. and she could've killed/seriously injured someone and not even really meant to do it...or been killed when she jumped out of my truck (broken her neck, got caught under my rear tire, etc.). Then suddenly I'd be facing a police investigation and possible vehicular manslaughter charges for trying to do the right thing on top of the mental/emotional anguish of having someone you know die right in front of you (PTSD is a mother to deal with, speaking from experience). The worst thing is she would blame others for setting her off or not stopping her instead of seeking help for the problem.
I think the biggest deciding factor on the subject of dating someone with a mental illness is whether or not they're seeking help for the problem. If they're ignoring the problem or not trying to work on it, I'd really rather not deal with it (You can't help someone unless they're willing to help themselves, oftentimes you'll be dragged down by it if you try). If they are seeking help, and depending on how the illness manifests itself, I'd be more likely to stick around and offer them love, support, and encouragement.