IIRC, BBCA aired Doctor Who the same day as the BBC last season. That hasn't been the case most years past, though. As far as I can remember, the "one week behind" thing has been the norm, at least for Doctor Who.
Since 2005, months at first, then weeks by the time series 5 rolled out (though the End of Time was only one week behind).
A Christmas Carol was same day as was all of series 6. Indeed, the need to go online for new Who has decreased. (Although I would buy the season sets when they became available to pay my dues to ensure more were made).
Back during classic Who, a few PBS stations aired some late season 1980s stuff before the BBC due to special agreements.