I think that the fandom heard through the grapevine that Ilya "admits" that Shane is the better player in TLG and people who have never read the books have run with that a little too far. For clarity's sake:
Ilya does say that Shane is better...one (1) time. He doesn't say it in public, and he doesn't say it gleefully or gladly or proudly. It's not a happy moment. It is, in fact, kind of tense and awkward.
Ilya says it after (A) Shane beats him by 0.13 seconds in the speed skating competition (so, to be clear, Ilya is not lying when he points out that this is basically a tie; it genuinely is very close) at All-Stars 2021, and (B) he has a kind of upsetting conversation with Scott wherein Scott jokes that the Centaurs are still nothing despite their recent success, specifically compared to Montreal of all teams, and also wherein Ilya asks Scott about gay married life without being able to tell Scott that he himself is about to get gay (bisexual) married. IMO it's heavily implied by these two events occurring back-to-back that Ilya is experiencing a depressive comedown from the highs of getting proposed to and going on a winstreak. This is RR's (admittedly kind of clumsy) way of showing that Ilya's depression isn't magically cured by The Power Of Love, and that all of Shane and Ilya's problems aren't solved by the proposal. Ilya experiences a high (proposal, winstreak) and then gets "slapped down" (losing the All-Stars comp, Scott jokes that the Centaurs' recent success means nothing, relationship is still a secret for now) and feels bad again.
Ilya sort of sneaks it in (he says "Can I tell you a secret?") while he and Shane are having sex, specifically while Shane is facing away from him and ~distracted~. Again, it's not something that he's announcing loud and proud. He can't even say it to Shane's face.
SHANE PROTESTS. MULTIPLE TIMES. Despite being distracted and clearly unable to think straight, Shane is confused and kind of alarmed: "God, why was Ilya saying this? Did he really think so? Did it matter?" (Immediately after asking if it matters, he protests again, thus answering his own question; it clearly matters to Shane.) This is not something that Shane considers accurate.
The whole point of Ilya saying that Shane is better is that it's jarringly out of character and not really based on anything. Ilya says it because Shane beat him one time by a single tenth of a second in a skill that, Ilya mentions earlier, Ilya is usually better at (i.e., this is not a representative result). When he tries to double down, he says that Shane was always the better player, which is just straight-up demonstrably untrue; Rachel Reid was really, really deliberate in balancing Shane and Ilya's accolades in Heated Rivalry, so we can be pretty damn sure that Shane and Ilya were equals pre-Ottawa move, at least. Ilya is for sure wrong when he tries to say that Shane was always better, if nothing else.
SHANE DOUBLES DOWN ON PROTESTING. He insists that they're tied, and Ilya agrees. Conversation ends (or, rather, shifts to the "Marlow almost hears them" smut lmao).
Takeaways:
Ilya saying that Shane is better probably has more to do with his depression than it does with reality. We are given no indication that this is a true and objective fact. It falls in line with Ilya's other depression-related self-worth issues in thinking that he's a bad partner/friend/teammate/captain, which we know are false.
Ilya does not and probably would not ever say this loudly, publicly, or proudly. This is a shameful thing for Ilya, who relishes competition and --- before the worst of his depression --- used to be incredibly self-confident about his hockey skills. It isn't #goals or "WAG Ilya" behavior.
Shane absolutely does not accept Ilya saying this passively. He believes firmly that they're equals and simply Will Not Let It Go. Even if Ilya did for some reason assert publicly that Shane was better, Shane would absolutely not let that stand. He would probably actively disagree.
IIRC, no other character ever agrees with this take. There's no widespread belief or opinion amongst unbiased characters that Shane is a better player than Ilya. It's not an objective fact or common opinion.
"Shane and Ilya are equals" is literally the entire premise of their relationship. Their original book is called Heated Rivalry. The fact that Ilya is unable to believe in the fundamental premise of their love and the thing that brought he and Shane together is SAD, y'all. The man is depressed.
