That's a good point. In case of an EC tie the process moves to congress,
who elects the president. This would still be considered a valid election.
I think part of the difficulty is just stating what is a "constitutionally
valid" legitimate president. Any attempt by any president to stay in power
would be backed by *some* legal arguments, whether spurious or not, which
we shouldn't be trying to adjudicate between here.
We could say "accepted by the speaker of the house and the senate majority
leader." Then we're getting a lot more murky. Or we just make that specific
case explicit: "having been awarded a majority of the US electoral college,
or elected by congress in case of an EC tie."
I'd prefer the latter, since it ought to be unambiguous.