Yes, but it's an argument that just goes round and round forever. Conservatives think the BBC is run by a left-wing cabal. Leftists think it's an establishment mouthpiece run by the Tories. We've been having exactly the same argument since the 1960s.

The Chair, DG, and other higher-ups will almost always have either Labour or Tory connections, because those are the two main political parties. You'd be hard pushed to find a suitable candidate that wasn't connected at a high level.

No doubt you've dispassionately gone out of your way to assesss that evidence and after detailed examination decided it's invalid. Which would be a perfectl reasonable step to make - if that's what you did. Did you?