There is an important nuance here in that it assumes that all employers understand that someone being fired can just mean that they weren't a good fit for that particular position. I'm not sure that is universally understood. I would be that most people still look at firing as an indication that the employee is no good. That isn't necessarily correct at all, but unfortunately I do think it's how the majority of people perceive things.
I have some issues with the "fire fast" philosophy, but this is not really one of them. Companies don't generally even divulge that they fired someone when giving a reference. They will say the employee is "not eligible for rehire," which is frequently code for "we fired this person for cause," and is generally interpreted that way. I do wish they would just come out and say that the person was terminated for cause, so others wouldn't have to guess, but that's not even really related to the "fire fast" issue.
Yes, and given that being without employment (really, without income, but those are equivalent for most people) for long enough is literally a life or death situation, you're fully justified in that by lying about it in self defense. If you're privileged enough that not having any income for an extended period isn't a big deal, then, so what? But, if you aren't, lie.
You don't need to lie, but you also don't need to disclose every single thing to your new employer. If you had a short stint at a company, just leave it off. If they ask, just say you took some personal time to figure out what you wanted to do next. I think that's a totally valid description of trying a new job that didn't work out. I know a lot of people who have taken years off for fun. No one questioned it.
"Fire fast" can mean you get canned after a 6 month probation period (I know I was at one place). Explaining a 6 month gap is just barely possible if you leave it off, two of those in a row and it's a substantial chunk of anyone's career.
That's a two way street. An employee who knows he'd be a better fit in some other position should proactively agitate for it, rather than hoping the boss will guess it on his own.