This is where things get difficult.
There’s no doubt that the ECA expects Congress to be applying a legal standard to the facts as they’ve been presented to them. That’s their duty — to act like a court.
But Congress is not a court. And it’s incredibly unlikely that any court, including the Supreme Court, would ever tell Congress how it must vote.
Here is an extreme case: Louisiana is a solidly Red state. President Trump is forecast to win that state by about 57% of the vote. But Louisiana has a Democratic governor. So imagine after the people have voted, the Democratic party insists that the election was rigged, or COVID blocked Democratic voters from participating, or whatever. And based on those arguments, Governor Edwards certified a Democratic slate of electors from Louisiana. Both slates, or groups, of electors gather on December 14 and vote. Both send their votes to Congress. On January 6, Congress gathers to count the electoral votes. When they get to the state of Louisiana, they discover two slates, one for Trump and one for Biden, but only the slate for Biden bears the Governor’s signature. Two members (one Senator, one Representative) object.
Assuming the Senate is still Republican in the new congress, and assuming Congress then behaves in a completely partisan way, we’d expect the Republican Senate to vote to support the Trump slate, while the Democratic House would vote to support the Biden slate. That means there would be a tie between the two. Under the rules of §15, it is the Biden slate that would prevail because it is the slate signed by the Governor.