Except that they don't early on in the game. I was in a situation that forced a restart, because while I had plenty of party members, three (of the initial four) of them were getting treatment, and that left me with exactly four party members to choose from after recruiting the only available hires. Of the available four, two of them wouldn't work with each other, which put the actual party size to three.
I went back to the coach, and it said that there were no more available to recruit at that time.
I think the game was actually counting all four of the available members, so as far as it was concerned I had enough. The problem wasn't until actually trying to form a party. I had to restart the game to avoid that shit. Didn't know about the backer heroes either.
Although I'm not sure how much longer I'll play this game anyway. Early on it's the antithesis of "fun", and it's not challenging in the slightest. It's 95% RNG based due to the way you accrue massive amounts of stress and have little, to no way of reducing it. I already have three people in recovery, and on my latest dungeon, I've had two members go from two ranks of stress to full and both went crazy. I even have two ways to reduce stress, but it doesn't matter. The first member to go crazy kept raising the stress levels of everyone else, and they are almost all at max. I don't have the patience to play disposable heroes, where none of them matter and you're just throwing resources at the game until you are lucky enough to progress.