Charlie, you are right it is oxymoronic and Steve, it is my feeling that you are wrong, it should not be changed to Wild Garden Thyme, and not just for the very simple reason that it is an oxymoron.
I am a field botanist, not an horticulturalist, but I am also a native english speaker and the term Wild Garden Thyme suggests a plant of cultivated origin which has naturalised in the wild. Surely this is not the case for Thymus polytrichus which is listed by BSBI as native. I have not checked, but I would be very surprised if Garden Thyme were not at the very least a cultivar of Thymus polytrichus, or possibly a hybrid between two or more wild thyme species, one or more of which may not be native. The truth of the matter must surely be that there are dozens of distinct variants of Garden Thyme, mostly of obscure wild origin.
Rob Large
Wildlife Sites Officer
Wiltshire & Swindon Biological Records Centre