Sometimes BBC film-crews will produce things for ITV and vice-versa, due to a number of reasons (such as convenience, capacity, logistics, technology, studio limitations, sometimes even cost etc...). A popular example of cross-production was The Royle family, whereby ITV (Granada) produced it for the BBC. Of course it happens more often on general things and even News
footage etc, that the public won't know about.
So it could well be that tbh.