I would suspect that the Standard refers to the general area where the television centre is ie Shepherds Bush. I can't imagine there are signs saying you are now entering Shepherds Bush please drive carefully and exit signs 300 metres up the road saying you are now leaving Shepherds Bush and entering White City please continue to drive carefully.
To me White City means the Dog Track where the Greyhound Derby was held, and the home of the Olympics in 1908 if anything, so a general and oft-repeated media reference to the BBC at Shepherds Bush, just like the Standard "lazily" or "imprecisely" did, doesn't really matter and I will not condemn the Standard for it and continue to regard it with the same reverence as I do the Newcastle Evening Chronicle.
Should you wish to correct such a clear and obvious error of journalism, then you may be in a bit of confusion whether to write to the new editor Emily Sheffield, or the former editor now demoted to editor-in-chief George Osborne. Maybe cc George Osborne because it occurred on his watch as editor, but as courtesy send it to Emily.
I do hope George wasn't forced to step down as a result of "Shepherd's Bush Gate"
George Osborne stands down as editor of Evening Standard
He will be replaced by Emily Sheffield, who is the sister-in-law of former prime minister David Cameron
I'm sure there was quite a rigorous interview procees to land the job, maybe over Sunday lunch