Yes, that's exactly right...a tooth can turn color when it's "falling out". See a dentist and in some cases they can numb the area and remove the tooth. When your child's tooth starts to get loose...wiggle it and pull it out when it's loose enough...NEVER wait for it to fall out itself.
Hope this helps!
-Jessica, Registered Dental Hygienist
The tooth and illness may not be related. My daughter's tooth turned grey as well when it was loose. She happened to have a dentist appointment and the dentist said that it was because there was no more blood going to the tooth. Just to be on the safe side, you may want to get her checked out. I totally understand - seeing the grey tooth makes you think all kinds of things.
Seeing a dentist is advised.