Actually it's very easy and logical! Fischer played 8 games against Korchnoi. Score was 2 wins for Fischer, 2 wins for Korchnoi and 4 draws. Fischer had an EQUAL SCORE against Korchnoi in classical time control games.
Karpov played 108 classical time control games with Korchnoi. Score was 31 wins for Karpov, 14 wins for Korchnoi and 63 draws. Karpov scored MORE THAN TWICE as many wins against Korchnoi as korch did against him!!
People need to get real. Fischer wasn't the antisocial ***hole people make him out to be...he had his good and bad moments like anyone else and being in the public eye, his bad moments were recorded. Likewise, Fischer wasn't a chess god! Kasparov and Karpov were better than Fischer. Fischer is an all time top 10, maybe top 5...maybe.
Lackadaisical analysis.
The regulation games were:
1960 Buenos Aires, 1/2-1/2 draw
1962 Stockholm Interzonals, 1-0 Fischer
1962 Curacao Candidates Tournament Rd 5, 0-1 Korchnoi
1962 Curacao Candidates Tournament Rd 12, 1-0 Fischer
1962 Curacao Candidates Tournaments Rd 19, 0-1 Korchnoi
1962 Curacao Candidates Tournament Rd 26, 1/2-1/2 Draw
1967 Sousa Interzonal, 1/2-1/2 Draw
1970 Rovinj/Zagreb, 1/2-1/2 draw
(This does not include several tournament 5-minute rapid games played against Korchnoi)
The point being, both of Korchnoi's wins over Fischer came in the 1962 Candidates Tournament, where Fischer accused the Soviet players of (and they tacitly admitted) collusion. The system was changed after this cycle to knock-out matches.
Fischer was 19 years old at the time (Korcnoi was 31 and in is prime), and played at a serious disadvantage - the Russians being ordered to take him to the limit every game, after his brilliant Interzonal.
This is to take nothing away from Korchoi, who was certainly one of the all-time greats (and he too suffered from at the hands of the Sivet chess machine). It simply points out the weakness in your comparative argument.
"Fischer and Anand shared the connection of being the first "great" chess players from their own countries."
Anand sure was, but Morphy, Pillsbury, Marshall, Reshevsky and Fine were not too bad.