He's made it up. The BBC guidelines do, expressly, state:where is this statutory obligation, or have you just made this up? And what does "impartial" mean? He may not have a professional responsibility to be curious about the government's behaviour, but does that mean he has no rights to express an opinion about it on any medium?
Lineker's lack of contrition suggests to me that he, and his legal team, are very confident he hasn't gone beyond what his contract allows. The fact that Tim Davie has spoken of him in glowing terms, and says that he wants him back in the fold ASAP, would seem to support this assertion.'The extent to which a non-staff member, contributor or presenter is required to comply with the editorial guidelines will be set out in the BBC’s contractual relationship with them.'
Then again, perhaps Tavy and Jinx have sight of Gary's contract and know otherwise lol.