The background colour of the bobcat varies from ‘buff, brown, reddish or yellowish brown to light gray and is streaked or spotted with black or dark brown”. So, yes, bobcats can have a grey or greyish background colour but it’s shaded and varies somewhat across the flank of the cat. There is quite wide range of background colours. But the Latin (scientific) name for the species Lynx rufus tells that the fur commonly has a reddish tinge. The Latin word ‘rufus’ means red, reddish or ruddy. In fact, the bobcat has been called the red lynx.
This medium-sized wild cat, about twice the size of a domestic cat, has a mottled appearance. The fur on the belly and the insides of that legs is white with a dark brown or black spots or bars. The quote comes from Wild Cats of the World by Mel and Fiona Sunquist (a highly recommended source). I hope they can find the time to update conservation information as the book was published in 2002. A lot has changed in terms of the conservation status of all the wild cats since then.