There's no doubt that Sheik's edgeguard is one of her best strengths, and Fox/Falcos do have pretty predictable recoveries so that only makes it easier for Sheik to win on those respects. However, it's much likelier for space animal players to start up some kind of combo against her than vice versa. For Fox, shines aren't fool proof, but then again, it's not exactly necessary for Fox to always waveshine out for a grab. If players start noticing patterns or realize that the opponent is frenetically trying to DI out so they can go for a d-smash, Fox players can always just jump cancel the shine and then come down with a falling u-air or just CC, tech, and rush in again. And Sheik can't exactly DI violently left or right during U-air barrages, so this will inevitably end up with Sheik getting comboed to decent percentages.
As for Falco, according to guys like pros like Dope, if you play Falco and can't beat a Sheik, chances are you aren't a real good Falco player. And this is a guy who gets to face off against Drephen (albeit he has an extremely unorthodox style Sheik) and goes up against other highly skilled Sheik players from all over the US.
Also, unlike characters like Captain Falcon or Marth, space animals have the luxury of not needing to end all their combos with a strong finisher. Because Fox is so agile and Falco is so oppressive with his lasers, they aren't as pressured into completing their combos with an u-smash/f-smash or whatever. And because their style of movement captures the pace of the game and forces it to be played in their favor, it's expected for them to be able to be more patient before they can land a surprise Bair/Nair/falling u-air/whatever.
You look the other way around, and most Sheik players are more or less forced to adapt to the way the Fox/Falco players want to play. Also, sheik players have to work a lot harder in order to start off combos, and her attacks really aren't effective until she can get the Space animals past 60%. And even after that, most players by now know where to DI from f-tilts and dash attacks. And unless they're playing on FD or other large stages, the chance of Sheik players getting long strings of combos on the space animals isn't as likely since players will recognize that the f-tilt/dash attack sends them up at about the level that most platforms are.
Also, it's not really fair bringing in Japanese and European pros. :/ For one, the space animals game in Japan isn't revolved around the technical aspect so much as the American game is. Instead, it seems more . . . reactionary and has higher reliance on reading opponents and attacking with aerials then long shine combos. Also, the Japanese even consider the space animals to have a leg up on Sheiks which is why players like Kei have opted to switch to Fox (OC2) while Sheik players (Shu comes to mind) have decided to pick up strong secondaries in order to play against the Space animals (in this case Marth). The only Japanese pro that seems really unphased by it all is Captain Jack. But Captain Jack really doesn't have M2K, KDJ, or PCs to face off against. Where as for Europe, it's PAL so it's not exactly fair comparing the two. :/ I mean, Falco's spike isn't always a spike and Fox can't kill upwards as well. In fact, I remember one time FlowinWater said that there's no way he could play PAL's Falco since it was just too different for him.
And yeah, stages to have a lot to do with it, and Sheiks are expected to win on Battlefield, definitely brinstar, DK64, maybe Dreamland (iffy, but I'd say definitely on that if it's Fox), and maybe even FD. But aside from that, I don't see Sheik having too much room to work with.
As for the Marth thing, Ken is the most standard example of what a good Marth can do, but Azen's Marth managed to take over at MLG Orlando (?) also, and he gave Ken a scare up in New York. Also, Mew2King's actually got a very strong Marth and managed to take out both Ken and Azen. Also KM and Neo have been pretty impressive and tear apart the East Coast pretty regularly, but they don't travel near as much. And as for foreign players, there's still always Ek who's number 2 overall in Europe or something.
So, idk, I'd say that even though Sheik is enjoying a lot of popularity right now, I think that Marth's game is still really dominant. And at least for my smash theories, I'd list Marth as having more matchups in his favor than for Sheik.
. . . But then again if you would've asked me a few months back, I'd have said that Peach should be ahead of Sheik so idk. I change my mind pretty quickly