The rule is against running in the government operated primary, losing, and then running in the general election.

The Presidential preference primaries are run by the parties. But the regular primararies are run by the state. Parties can choose to use the primaries or not. If a Party chooses to use the primary, then all candidates must pay a hefty filing fee, collected by the state to finance primaries.

If a party instead chooses to nominate by convention, then there is no state-mandated filing fee. If the party has ballot access, the candidates they choose in convention are put on the ballot.

As far as I know, there is no rule against seeking the nomination of multiple parties in convention, losing in one, but appearing on the ballot for those whose conventions are won.

Of course, the “rule” really focuses on candidates who lose the primary in June, and then collect signatures for an independent run (usually due in August) or even promote a write-in.