This is a fun debate.
The room might not be owned by the ladies or the men, but it is to be used by the ladies or the men, therefore the possessive still applies.
Compare:
"The teachers' staff room."
This is not correct in my opinion because the teachers do not own it. They only use it as a collective group, therefore it should be described as a "teachers room." We may be used to seeing it written as
teacher's, but "teachers" is clearly a modifier to the word
room and seems more correct as such than a possesive. The teachers use the room but do not have custody of it and cannot use it however they like but only for the purposes that someone else designates.
This is correct. The human may technically own the bed, but the owner has bestowed ownership to the cat and the cat is free to use it however it chooses. And anyone who has owned a cat, knows that cats
do own things, lol.
"The children's television shows."
This one is definitely trickier to explain why it is correct. Naturally the children do not
own the shows in the conventional sense, but they have claimed them as their own, in their own capacity to do so. By stating it this way, the children lay claim to the shows they like to watch. Also, using it in this manner indicates a specific set of children and not children collectively. Their shows might include "Law and Order" or "Supernatural," but these would not be considered
children shows (notice how a word not made plural with the addition of an "s" complicates things).
"My husband's company car."
This would be correct because the company has bestowed custody of the car to the husband and in this case would indicate that he has the sole use of it. In essence, he owns it and is responsible for it. Nor would you have a
husband company car. Using
husband as a conventional adjective would not make sense. Now, just as in the case of the teachers, the husband cannot use the car except for the purposes designated by the company, but in this instance, the thing in question is portable and is placed in the care of one person and has sole responsibility for its use and can essentially take it wherever he wants. The implication by the terms of its assignment to this individual indicates it is
his for all practical purposes. I think it could be referred to as "the company car" or "the company's car" and either would be correct.
The teachers/cat/children/husband in the above sentences do not own the room/bed/TV shows/car - but they use them. Therefore the possessive is still appropriate.
I know my use of italics and quotes may be all over the map, but after all the thought given to this, my brain is not up to the task of sorting this out. So sue me.
By the way, how do you get the highlight to work when you split someone's quote up? Nevermind, I figured it out.