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. I suppose the tell is whether people who are up in arms about Tory Richard Sharp were similarly upset when Labour-supporting Michael Lyons or Gavyn Davies were chairman, or when Labour-supporting Mark Thompson, etc were DG.