We have strict standards and procedures that our deli teams are to follow which include temperature checks that are documented on cooked birds with a calibrated meat thermometer.
It is possible to encounter red or pink color in a fully cooked chicken, the only real indicator of a fully cooked chicken is temperature, color does not indicate doneness. I know this seems odd as we have always been told to cook until it is no longer pink but that isn’t the case. The USDA explains that even fully cooked poultry can sometimes show a pinkish tinge in the meat and juices. This is particularly true of young chickens whose bones and skin are still very permeable. The chicken's feed and whether it's been frozen can also affect the final color.
If you were seeing a deep red color or fluid resembling blood around the bone, pigment in the bone marrow can color the surrounding tissue and make the bones themselves look very dark. This is typically a reaction between the solution that is injected into the bird to make it juicy and the blood vessels surrounding the bone.