Inventing the wheel

I was musing last night about the oft repeated statement that if it had been left to women we'd still be living in caves. But how do they know? How does anyone know for example that it was men who discovered fire, smelted metal to produce weapons and tools or invented the wheel? The answer is of course that no one knows who invented/discovered these things. I imagined this scenario:

Caveman: That mammoth isn't where I left it this morning. What have you done with it?
Cavewoman: I had to keep climbing over it so I got together with the neighbours and we moved it
Caveman: (Snorting in disbelief) You're just not strong enough to move it even if you all get together. A man must have helped you.
Cavewoman: Believe what you like - we moved it.
Caveman: (Scratching head) Well show me then.
Cavewoman: (Hands on hips) You don't believe me?
Caveman: I can't see how you did it.
Cavewoman stumps off to the other side of the clearing and points to mammoth - skinned and partly dismembered on a platform of round logs and matting.
Cavewoman: (Pointing) Like this. You just have to push it then you can move it wherever you want it to go. (demonstrating)
Caveman: So how did you manage to attach the mat to the logs?
Cavewoman: Reeds - how do you attach the thatch to the hut stupid!?
Caveman: That's really good I'll have to tell the lads - but I'm sure you women can't have done it without the help of a man.
Cavewoman: (Stomps back to the hut in disgust muttering about nothing getting done if it wasn't for women)

Could it have been like this? Who knows and we'll probably never know but this is just as likely as a man inventing the wheel. How do we know it wasn't a co-operative effort as many scientific advances have been?