Well, it wouldn’t necessarily be obvious, like in a “FORM 883-A: Disclosure of Ties to Russian Oligarchs.” But remember that the one thing the great global hegemony is good at doing is tracking money, and where it impacts taxes, governments are very good at noticing.
So, what would “ties” to shady Russian billionaires mean? In Trump’s case, that they were loaning him money (or maybe bribing him, or loaning money with the anticipation that it would become a bribe by virtue of forgetting the loan later on). And for that money to be useful to Trump, and not just gathering dust in a Moscow vault, it’d have to enter into his financial bloodstream.
A direct loan from Ivan Badguyovich to a Trump business, or Trump himself, would show up in bright red letters. (You can’t sneak huge amounts of money into the system unless you’re also committing massive money laundering, which would be more trouble than it’s worth at Trump’s level. Think the “warehouse full of cash” situation from Breaking Bad–pretty accurate.) And maybe that shady-looking (but legal) loan is right there for all to see on Trump’s returns. That would be a reason he might not want to release them.
But maybe Mr. Badguyovich covers his tracks a bit, using shell companies and cutouts and all other manner of financial trickery. Even that starts looking awfully bad. Why are all these weird companies nobody’s ever heard of lining up to loan Trump money? Your eyes and mine might glaze over, but people who know this stuff would be screaming bloody murder about it.
tl;dr: even getting legally bought by incredibly skillful buyers is extremely difficult to hide… if people can look at your tax returns.