Other way around I think and so I've read/heard.  Domestic cats retain their
kitten like qualities and treat us as providers (mother) for food, heat,
water, comfort, stroking (which is comparable to a mother licking it's
kitten) and general companionship.  Cats who have a really deep bond with
the 'parent' will often respond by bringing back presents, which in a cats
view, is things like dead mice, birds and other assorted wildlife (my cat
once brought home, amongst other things, a full dead coy carp - never did
find out where it came from).  They leave such presents on the back step or
on the lounge floor, completely untouched, apart from being dead.

Like any child, cats are good at getting our attention when they want it and
completely dismissive when they don't.  You can experiment on a cats psychy
by how you respond to a cat when it walks into a room.  If you try and give
it loads of fuss and draw their attention when they walk into a room, they
will more than likely not respond, or respond initially and then just walk
off.  However, if you completely ignore a cat when they enter a room, and
avoid any sort of eye contact, the cat will respond by coming up to you,
meowing, and trying to grab your attention by rubbing around you until you
respond.  This is especially so when you've got visitors, which is when the
cat is saying 'hey, look at me...and introduce me'.

I've noticed with my cat that they can and do often respond to emotion,
especially crying, pain and upset.  During time of distress, especially for
example, the time of death, cats sense something is awry and will respond
with more affection and the comforted becomes the comforter.

It often amazes me how cats respond to other changes, such as when moving
house or even going on holiday.  My cat has associated seeing suitcases with
going to the cattery, even if I get the cases down from the attic several
days before I go away.  The cat becomes fairly agitated and spends as much
time out as possible.