If he got it from the wikipedia site then he misread it. He probably heard it on a MINI forum or through a MINI club newsletter or something. The Triumph nameplate, as much as I would like it to be true, had no bearing on purchasing the Rover group which is how BMW got the Mini.
BMW still owns the Triumph name and there was great speculation in the last year about a new BMW, possibly MINI based, sports car carrying a Triumph nameplate. The last I read on the subject, the BMW dealership network shot down the idea because of BMW's own dealership franchise rules. Any non-BMW badged car has to have a separate building. Which meant that any BMW dealer that also wanted a MINI dealership had to build a new showroom specifically for MINI and could not mix the BMW and MINI showrooms. Which is also why not every BMW dealer can sell you a MINI. The same rules would have applied to adding the Triumph nameplate into the mix. Dealership owners weren't very keen on building a third showroom and BMW wasn't willing to allow other nameplates in a BMW showroom. Even if BMW owns the other nameplates.
I'm afraid for the time being BMW has no interest in either using or selling the Triumph nameplate.