Cards that can normally be cast from exile don't have the ability to be cast from there without paying their mana cost

If you exile Squee, the Immortal with Idol of Endurance and then activate it, you should be able to cast it for free *or* for 1RR from exile.

Unfortunately, you can only cast it for its regular cost of 1RR.

This is likely a bug with all such effects (Idol of Endurance, Hazoret's Undying Fury, etc) and all cards that can be cast normally from exile (Squee, Misthollow Griffin, Eternal Scourge)