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The thing is that, even if you could sign a message to prove ownership over the address (such as you can do with bitcoin if you have control over the private keys), that does not prove that the other account is not related (i.e. an Alt account).
Conceptually, come the case, one would need to prove that those two accounts are either one and the same person, or two separate people. Common addresses between two accounts is often due to Alts using the same address to receive their crypto. The issue arises when those accounts participate in the same campaign simultaneously, likely breaking the campaign rules, and if not, ethics.
Way more often than not, those two connected accounts are likely Alts, but someone could get caught-up mistakenly (people may copy/paste other people’s submissions, and forget to change the address). It’s really a reputation issue on the surface, lest one of the involved accounts be a banned account, which may even lead to banning all the alleged Alts.