That analysis ignores who the Third Party candidate is: A popular leftist Third Party candidate would indeed take votes from the Democrat and help elect the Republican. Likewise, a popular right wing candidate would take votes from the Republican and help elect the Democrat. In general, a Third Party candidate can only help elect the mainstream candidate the least like them. This is why people say Third Party runs can only hurt their cause.
It would be completely different if we had a parliamentary form of government, where a Third Party could form a coalition with the mainstream Party most like them, But we don't.
I say you're correct in your synopsis. The reason I stated third party candidates usually hurt Republicans more is that the Libertarians are on the ballot in all 50 states presidential wise. They also run candidates for governors and senators. Most Libertarians would vote Republican if limited to just the GOP and Democratic candidates.
Johnson received 3.28% of the total vote in 2016, Jill Stein 1.07%, McMullin 0.54%. Libertarian and Conservative votes to Johnson and McMullin dwarf Stein's. My word usually doesn't mean every time, just most of the time.
It's high past time that we start electing Americans to congress and the presidency who put America first instead of their political party. For way too long we have been electing Republicans and Democrats who happen to be Americans instead of Americans who happen to be Republicans and Democrats.