Derech Hamelech,
No, I don’t have a Rishon to back me up. But I have spoken to quite a few Orthoprax people who have nothing to gain and only to lose from not believing. Most of them are married with a few kids and would not break up their family for their disbelief. They don’t think anything in the outside world is worth giving up their family, even if it means being orthodox in practice without belief (why would they give up their family for a cheeseburger?).
I quickly flipped through the link you posted. Its a nice kuzari-like explanations but there are logical ways around that.
The Orthoprax people I know are VERY learned. They probably know more Torah than most people. They kept studying and learning and looking to believe and couldn’t find it. Without any motivation to not believe.
So maybe Rambam was talking about in general. But there are always exceptions to the rule.