FIDE didn't establish the championship. Steinitz did. That's not a generalization. It's a historical fact. The title passed on from one champion to another when a match was played with the title at stake -- the title was part of the winner's prize fund. Alekhine died while he held the title, as did Fischer, so in both cases other means were used to decide who owned the title after the death of the current champion (a tournament was held when Alekhine died and by default the FIDE Champion of the World of 2008 is the commonly recognized WCC today). But the ownership of the title never passed to FIDE.
Fischer made a distinction between a FIDE granted title and the WCC. He resigned his FIDE title, but he never surrendered the WCC.
"As I made clear in my telegram to the FIDE delegates, the match conditions I proposed were non-negotiable. Mr. Cramer informs me that the rules of the winner being the first player to win ten games, draws not counting, unlimited number of games and if nine wins to nine match is drawn with champion regaining title and prize fund split equally were rejected by the FIDE delegates. By so doing FIDE has decided against my participating in the 1975 world chess championship. I therefore resign my FIDE world chess champion title. Sincerely, Bobby Fischer."
FIDE didn't accept this resignation, but instead continued to negotiate with Fischer. So, in any case, Fischer's resignation is of no effect. The FIDE title was granted to Karpov by default when Fischer forfeited, not when Fischer resigned the FIDE title.
As we have seen when Kasparov broke away from FIDE, Fischer's distinction between the WCC and the FIDE title is more than an academic or philosphical difference. FIDE doesn't own the WCC and, until FIDE can win the title from the WCC under terms that the WC agrees to, FIDE will never own the WCC title.
As Fischers' letter states, he resigns the WC title and no longer, in his mind, has claim to it! It does'nt matter whether FIDE accepts it or not! Therefore it is up to the bodies that be to figure out how to continue.
The point is that Fischer resigned the FIDE WC title. He never gave up the classical WC title. Fischer insisted on his right as WC to choose when and where and against whom he would defend his title.
How did Fischer have that right ? His predecessor didn't. If Spassky had been making the terms, the challenger would probably not have been Fischer and the match would not have been played in Reykjavik. Fischer' title was obtained under the Fide auspices, it's not like the Fide suddenly came out of the blue.
so who own the classical WC title now ?