Modern, and even old, sensors absolutely can see stars during the day. It's really a question of magnification. When you magnify the image, the pixels a star falls on don't change much, but the background gets darker because the background is spread over more pixels.

I was talking to a grad student who was having an issue getting descent flat frames (images of a uniform field, used to account for dust and optical train effects). I asked why she didn't just take a picture of the sky in the daytime like most amateurs do, and she said she always ends up with stars in the image doing it that way. They tried finding the least populated part of the sky, but still always picked up stars.