I believe that the answer to the question is dependent upon how well the cat knows the person who is touching her kittens.
The veterinarian’s response to the question is that:
“..most queens (female cat mothers) display anxiety when their very young kittens are constantly handled by unknown people or if unfamiliar pets or other household animals they are not comfortable with are allowed near the kittens.”
The conclusion here is that if an unknown human or companion animal interferes with a mother’s kittens then she may become anxious. Note: that after 6 weeks it is important that kittens do interact with unknown humans and companion animals to become socialised and develop acceptable behavior in the home.
The other side of the coin is that if the mother cat is very close to her human owner then she may well want to involve that person in the birth of her kittens and clearly will not display anxiety. Quite the opposite in fact.
On the website Quora.com, Franklin Veaux describes his experiences when his cat Kyla gave birth to her first kitten. As soon as the kitten was born the mother picked him up by the scruff of the neck and deposited him on his lap. The mother then crawled off his lap to have her second kitten. She did the same thing with that kitten. Afterwards, she picked them both up and carried them back to the bed that he had set up and began nursing her kittens.
It would seem that his cat wanted him to be involved. The kittens grew up to be great cats. They appear to be blue lynx pointed Siamese cats.
Also on the same website, Janelle Hayes, who describes herself as a crazy cat lady, said that her female cat insisted on giving birth to her kittens on her bed despite having prepared a cosy box with soft blankets for her. As soon as the kittens were born they were handled by Janelle or her daughter and “Mama didn’t mind”.
I’m sure that there are other examples where a queen fully accepts her kittens being touched by their human guardian/caretaker because they are very familiar with and close to them. They perhaps relate to their human caretaker as another female cat and it is well known that in colonies female cats often share mothering duties. That may be the origin of this behaviour between cat and human.
Note: Veterinarian’s quote: Pediatrics section of Cat Owner’s Home Veterinary Handbook 3rd edition.