I can only speak to what I did and am unfamiliar with Beartooth Mountain Guides' agenda.
I went with JHMG for this one as well and we had a fantastic four-day climb with a great cast of clients and great guides. On Day 1, we hiked up past Mystic Lake and up "Heartbreak Hill" to our first camp on the lower part of Froze-to-Death plateau. On Day 2, we moved across FTD plateau to our high camp on the far end of it. Day 3 was summit day and back to high camp. On day 4, we hiked out.
FTD plateau is pretty exposed to the elements and not someplace you really want to be in a thunderstorm, so maybe that was the objection that was raised. But there are lots of places to seek natural cover along the way if you pay attention to the sky and plan for it. We waited out some threatening skies on Day 1 in a position of safety. Storm never hit as it turned out but we would have been "safe" even if a little wet.