Elections are supposed to be decided by voters, not courts,

That is fine in principle. What election systems - and in particular
the "winner takes all" systems - do not take into account is the fact
that an election is a measurement, and as any measurement has an error
(which itself can be measured in various ways from the actual election
data). If the outcome is to be a binary decision, as in this case, and
the margin of error is as large - or, in the case under discussion,
substantially larger - than the difference that leads to the decision,
it seems appropriate to say that the election has had a random result,
because repeating it would in all probability lead to a different result.

So what the courts should have done is to select a person, have the
incumbent say whether he wants heads or tails, and have that selected
person throw a dollar to decide.

Jan