>>>> As I said, according to the three sources above, which are the first sources I clicked on which didn't seem like blogspam, the phrase "proof by contradiction" is a term of art which means "uses the law of excluded middle to conclude the truth of a statement given a proof that its negation is false"
In that case your "It's much dumber than that, since he's invoking the law of the excluded middle to use contradiction at all." is simply false: you can use contradiction to refute a proposition without proving that proposition, without using LEM.
(quote from you; my emphasis)