I have never heard of a PRIV holder being forced to buy a full-fare ticket on Grand Central, and a member of GC staff has stated:-
If by "privs" you mean your "boxes" then no,however if you bought a priv open single/return with your TOC card then it will be accepted as it is an inter available ticket !
My understanding is that GC will be happy to sell a PRIV-discounted ticket on board, and I've not heard of that changing. Back in the days of Valentas I often travelled on GC, and several members present on occasions held PRIVs and I never heard of any problems.
And yes, my understanding is that barrier staff cannot prevent you boarding another operators trains - unless there is an agreement between the TOCs that this can be done (which, for franchised operators, may be a franchise commitment in some cases, but for open access operators such agreements cannot be imposed on them). EC staff should be under instructions to let you through, and if they did not then that incident would need to be reported. I did hear of issues in the early days when GNER and GC had some 'disagreements' (!) but not heard of any issues at all for years.