"Its something that shouldn't happen no matter what."
It shouldn't happen all the time, but any car alarm is susceptible to interferance by other radio signals, they have to be to be FCC compliant. That's not to say that they can't encode the signal or use an alogarithmical (sp?) "code hopping" type of signalling process to help eliminate false alarms and/or accidental disarms/rearms (I don't believe subaru uses the code hopping in its OEM alarms.) Like I said, it should not happen every time your neighbour AND other suby owners use their remotes to unlock their cars. It sounds like it may just need a reprogramming or alarm module and keyfob swap. I do have a funny story to share on this matter:
I was installing a remote start/keyless entry system into a 98 Dodge Caravan and the owner asked me if it was possible to tie it in with his garage door opener so that the exhaust gases would not be trapped in his garage while it was running. I told him I could do it, but I would probably need to wire a relay to a door opener module to do it or I would have to buy an interface that is designed to integrate with garage doors, either way it would probably cost the same amount (I think I quoted $150 extra to do this). He said he wanted to think about it but to go ahead with the install w/o interfacing. No problem, I get his remote start in he is very happy. About an hour earlier he calls and says "I thought you said you weren't going to hook this up to my garage door". I told him I didn't. He then told me to come over to his house after work and explain why it was working with it afterall. I thought he was pulling my leg, but he promised a cold beer for me if I came over so I went and sure enough the "start" button would open his garage door, but his lock and unlock buttons had no affect on it. That was one of the weirdest things I ever saw.