I really don't think it is the place of a company like BA (or Virgin Trains come to that) to become censors. I am not a fan of the DM mostly due to the rotten journalism, but unless it's for a commercial reason I don't think BA should restrict access to it.
I would respectfully point out that some of the campaigns by the DM I think we can all agree on were positive. I don't think we would have seen the justice we have in the Steven Lawernce case without the DM campaign