Question re: US&UK Passports

My two stepchildren leave in a couple of days to the states with their mother, to visit family. they will be staying for most of the summer break. 

Both their US and UK Passports had expired so their Mother went to the US Embassy to update their US Passports.  I VERY SERIOUSLY DOUBT she updated their UK passports.

So here's my question...They will be able to leave the UK and get back into the States just fine.  But won't they need their UK Passports to get back into the UK, since they live here?

Yes.

Yes, you will need to make sure they have both current passports.

And the myth continues...

There is NO requirement to enter the UK on a UK passport. 

And the myth continues...

There is NO requirement to enter the UK on a UK passport. 

However, that is their proof for right to live in the UK. They won't have a visa in their US passport.

Their expired British passports are equal proof, no?

I am not sure to be honest. I guess in my mind, I am assuming the children are travelling alone and the last thing I would want is any kind of extra headache for them to deal with. If at all possible I would want to ensure they have their UK passports also- but Sara could be very right and it might not be needed.

I thought that theoretically, if you can prove your British citizenship in another manner, then you do not need a British passport to enter the UK.