Soil stack venting issues
Mr Stephens, you better be careful. It's talk like that, that will send you down the long stinky road of being a full-time plumber! 

Jokes aside, I believe, from what you say, that you are correct. You may want to call the building manager and have them check the main vent(s). Each apt should have it's own smaller vent as well, but if this is a 20-year old apt building, it may be a remodel, where there wasn't enough access to vent every apt. The main vent may be failing for whatever reason, or the neighbor's you speak of could be failing, or a combination thereof.

If you smelled stink out of yours, you may be okay.