As a follow-up to this question, the answer there indicates that by the rules set by the Senate, a quorum is assumed to be present unless someone requests a roll-call vote. Because of this rule, the Palm Sunday Compromise was passed 3-0.
Under these same rules, what prevents a lone Senator from simply going somewhere by themselves, holding a vote on a bill, and then passing that bill 1-0? It seems safe to assume that such a thing cannot actually work in practice, because if it could then the entire system of the Senate would break down, with each individual Senator actually having the full power/authority of the entire body. But what would make such a situation legally different than the 3-0 vote that actually happened?