The Freedom of the North East page on National Rail Enquiries (
https://www.nationalrail.co.uk/times_fares/pr41c8ce0a04000400a1e4a874e98bb8.aspx ) shows that it is valid on rains operated by
LNER» , Northern, Trans Pennine and Cross Country. That is going to cover by far the vast majority of services - the only
TOC▸ I can think of off the top of my head that runs trains in the area and isn't mentioned is Grand Central - there may of course be others.
I suppose it's best to think of these rovers in much the same way as one would a bus equivalent. For example, First Bus may offer a "tourer" ticket of some kind essentially saying "pay us this amount of money and you can ride around on our services to your heart's content." However, to have that ticket also available on Faresaver or Stagecoach services would require an agreement between the companies to allow it and, also behind the scenes of course, an agreement between them over how to split the proceeds.