This is not true...yet. If you go active duty USAF, there is a chance (15% ?) that you will be assigned to UAV's in which case you will almost certainly never fly manned aircraft.

If you go navy, usmc , uscg you have a 50%+ chance of being assigned helos. Army is even higher.

The usual age limit is 28, maybe extended to 30 in timers of need (it varies by service also).

Waivers are possible, but very hard to get. You would probably have to have some unbelievable qualifications to explain why you waited so long...too busy training for the olympics, stuck on the international space station as a nasa mission specialist, etc. With that said, it cannot hurt to try, but the recruiters will not want to spend a lot of effort on someone who needs a hard-to-get waiver.

Army aviation might be a possibility...I think they had extended their age cutoff to 35 in the recent past. They are doing more fixed-wing flying these days, so while you would probably start in helos odds are good that you could get enough fixed-wing time to eventually get an airline job. Consider active duty, army reserve, and army national guard.

Also...be aware that military service (especially as an officer) is a much larger commitment than just an easy way to build flight time...better have some other reasons for wanting to do it.