No matter the context of the actual events, Milbank had no right to broadcast or expose what may have been said at the Heritage Foundation event.
It was open to the public and, in fact, lived streamed.
He wasn't there "under cover". He was there as a representative of the press. Unless requested to withhold some information "off the record" -- which he was not -- he is fully entitled to "broadcast or expose what may have been said at the Heritage Foundation event".
He's not entitled to lie about the proceedings, of course. Though, as a member of the press, he's legally free to do so. But let's not introduce a false premise into the argument. The media has a constitutional right -- if not an obligation -- to report events they deem newsworthy.