Generally a Resolution Advisory will only be posted if there is a probability of collision i.e. if you're at different altitudes there must be some convergent vertical speed.
Don't forget there are two software versions out there. The older Change 6.04 expects at least 1000 ft seperation and thus is more likely to bleat if you break that (as in the original post). The newer Change 7 is designed for RVSM and 500 ft seperation (we had to get within 300 feet for an alert during some sim testing). The one thing to remember is that if you have the later software and get an alert - react immediately - you're definitely on a collision course if you don't!
This software is produced by Mitre for the FAA so it doesn't matter who builds your TCAS you'll have the same results.