We won't do a recount unless we find illegitimacy, yet we won't find that, unless you do a recount. Isn't that the left's argument against voter ID's? (prove to us there is fraud before we can allow you to check for fraud.)
If something is found, then steps can be taken to re-store confidence in future elections, which re-enforces legitimacy in the system. If nothing is found, then the voting is already legit. It's a win-win situation.
Jill Stein's reasons are obviously biased, but we can use it to accomplish something positive.