I think that asking to stay another night, does require some explanation, since inviting yourself to an event is rude, and extending an invitation is rude, so doing so need to be explained. For example, if I invite you to dinner and you announce that you need to stay the night, I fully believe I'm entitled to ask why. Depending on your answer, I may or may not be right in declining to provide the additional hospitality, but to say that any request for additional hospitality must be met with a yes is just not the case. Perhaps it is JADEing, but then yes, you do have to JADE or you have to graciously accept a no, since a guest is not entitled to any and all hospitality they ask for.
"I suspect they either think she can't spoil Boyfriend in the manner they think is de rigueur for a potential wife (either by making all the money or by doing all the housework) or that it revolves around really nasty speculations about sex or kids", perhaps, but I don't know that most parents expect their son to be supported by their wife. It seems a huge leap from no you can't stay another night to this.
As an aside, we have all taken it at face value that the GF was in crippling pain and needed to stay. If making the leap that the parents are looking for someone to support their son is reasonable, the other possibility is that GF is an special snowflake who uses her disability to manipulate people. After all, we have gone from sitting all day caused her pain to she took all the right precautions, got up, walked around, etc, but the day of conversation was just too much and has caused her to need at least 2-days in bed to recover.