I am sure that they
could. They have just
decided not to, as you hint at.
For the record I am aware
@Bletchleyite has made the claim that they did before, although I doubt it even then. It has been said before:
www.railforums.co.uk/threads/nrcoc-replaced-by-nrcot-from-1-10-2016.135842/page-3#post-2713856
and it hasn't changed much since 2016.
East Coast briefed their staff to accept non-stopping splits with West Yorkshire products, but to reject them with a South Yorkshire product, on the basis that they do not serve any two stations in South Yorkshire and as such were never a part of the scheme in the way that they are in West Yorkshire. Even they excercised ignorance of the actual terms and conditions and the contracts they might be bound by, and put their commercial interest over them.
There's a commercial incentive for CrossCountry to make the claim that this combination is invalid, even though a brief logical analysis can result only in the conclusion that it
is. If they make an incorrect claim, some customers will believe them and pay a higher fare as a result. Hopefully yorksrob is not one of them.