Lord McAlpine's a whiney litigation happy martyr who's made big money off the BBC from milking his outrage. He did more than anyone else to keep the story in the headlines and without him constantly keeping it in the media, no one would have made the connection - from the BBC, anyway.
The BBC didn't even mention him in person, just suggested a Tory from the 1980s.
If advised of a Tory from the 80s, I and most would think of the high profile ones like Tebbit, Heseltine, Howe, Pimm, Keith Joseph, Baker, Hurd or Lawson. I bet if you asked 1000 people to name a Tory from the 80s (other than Thatcher), none of them would say McAlpine.
He's got £185k from the BBC for hurt feelings.
Only a few weeks ago, the Tories - the party that claims it's on the 'side of' the victims not the criminals, slashed compensation for victims of serious crime. The payouts were already a small fraction of the award McAlpine got for his bruised feelings.
As for Twitter, he sees another opportunity to grab some more compensation, keep the story in the press and play the martyr.