Naturally I haven't put any of these people to a lying detector, so this is more like mathematics to me: Simmons (the outnumbered one) is the only one trying to obscure it a bit. And his opinion is the furthest from the engineering staff.
I have never heard of re-doing drums for a live album. It doesn't sound practical, unless you want to redo the whole song (reasoning that the drums are the basis).* I have never heard of drummers redoing live recordings in the studio, but I am suspicious when I listen to Halford's Insurrection, because the whole thing sounds quite studio, drums included.
* Iced Earth's Days of Purgatory has some re-recorded drums, while some guitar parts were kept! But this stuff was played much more tight than live recordings by Kiss.