You would be correct. Its true that some have "their own definitions" and jargon to describe things. From an industry, accuracy, historical, grammar and military perspective its 1-5 generations using integers. I've had a chance to bounce this off of a lot of really experienced people just to get a peer review of this topic and to a man all agree. Its also undestood that when people talk 4.5gen or such its meant as a temporal reference and only as jargon/slang. The so called 4.5 gen platforms are those that are based on 4th gen designs but for what ever reason appeared and matured after the more established 4th gen platforms were all ready setting the standard and operational. The only thing it has to do with technology or capability is that the later arrival means technologies that would have been cost or technologically prohibitive may be incorporated. We see this in platforms like the F-16 Blk 60, CLEARLY 4th Gen, which has an AESA for instance. A feature common to 5th Gens. Its also been back fitted to F-15C's. Nobody calls the F-15C 4.5th Gen though. Similarly, the F/A-18C is one of the most versitile platforms in the world. Far more capable than some of the so called 4.5 Gens as a multirole platform. But is the F/A-18C 4.5 Gen? Of course not.
Also the fact that people have mentioned 4.5 gen in conferences is really proof of anything other than the fact that humans were present. In typical human fashion, jargon/slang has entered the vocabulary. I cant remember how many times I've heard Kevlar helmits refered to as K-Pot. Or Armor refered to as "Heavys". In short the military is full of jargon and slang. The F-16 doesnt even use its real name. But its still the Fighting Falcon.
Getting back toward the original question though. A 4th Generation aircraft is simply the 4th in a series of successive platforms designed to perform some role. For example F-86, F-100s, F-4, F-15(4th Gen), F-22. If the F-22 had been developed as a successor to the F-86 then I'd argue just as strong a case that its 2nd Gen. If it works different someplace else so be it but I havent been there.