Are inferior functions more rigid or really loose? I've read such disparaging takes on it I don't know what to believe in. Like this blogger who uses Hermione from Harry Potter as a great example of inferior Fi because she's fanatic about her freeing the house elves from slavery, but then also says ExTJs usually ignore their morals.
You're right this conception is wrong.
Some people actually integrate their inferior function into consciousness, which makes them quite open to it actually. Some people even repress or deny some of their higher functions, which makes them think they are a certain type when they might not be.
I've come to see someone who is SiTe ("ISTJ") with Ne developed (l--l) and a so-so relationship with their Te, and they surely don't come across as your typical ISTJ. They'd get typed high Ne in mbti/jcf for sure. And I've seen an NeFi ("ENFP") with Si developed, they also don't come across as your typical hyperactive RANDOM XD meme.
So, it depends more of one's relationship to their function than the hierarchy of their cognitive stack. However, usually, unless the inferior integrated, it's more common to have a certain rigidity regarding your inferior function or for it to be toned down compared to a higher placement even when there is integrated consciousness. The SiTe l--l I mentioned doesn't show as much scateredness as high conscious Ne. It's an Si ramble open to enlarge its cone of exploration and readily making Ne association, but with information stored in instead of straight out of the blue.
I'm late to answer this, whatever, I hope it still answered the question. You're welcome to ask anything else, despite the uncertainty of when i'll reply.