You are right to be paranoid about a new (to you) car. You are getting to know your new vehicle ... you just won't know about things, so ...
With that said, I'd say it's pretty uncommon for a "brand new" car to have a smell like you describe. If it truly was a burning rubber smell, it more than likely came from a belt, but could have been a lot of little things. A filter will not get warm enough for anything to burn off of it. However, the thing is, it's a new car. It obviously burned something off. If you smelled something briefly, it was there only briefly, and you didn't see any physical smoke, I'd suggest it did what the mechanic stated happened. Whether it came from off of a filter would be suspect, but it came from somewhere, obviously.
If the mechanic took a look and didn't see anything which looked like it was going to be an issue, and if the smell doesn't come back, there's no real issue. A new car should have an adjustment period provided by the manufacturer. If there's anything within the first year which rears its ugly head you don't like, you can take it back to the dealership for adjustment. If something happens again, you still have the option.
More than likely, your new vehicle is going to be just fine, but that doesn't mean you shouldn't pay attention to what it's doing. By paying attention you're just being a good consumer and vehicle owner. You don't want your new vehicle to go up in smoke, that's for sure! My suggestion at this point is, to keep doing what you're doing: drive your car; enjoy your car; pay attention to what your car is telling you. I'll bet you and your new go buggy will have many pleasant, trouble free miles ahead of you.