I don't think it was the corporate tax side that Bernie was worried about HMRC investigating. I think that was to do with his personal ownership, it's transfer to Bambino and Bernie's connection to Bambino. His tax arrangements were clean as long as he had no control over Bambino, the family trust that Ecclestone had set up in 1997 as F1's ultimate owner.
This control was important during a series of transactions between 1999 and 2006 when Bambino sold chunks of shares in F1. Bambino had to exist at arms length from Bernie for the tax break on the original transfer to be valid.
Gribkowsky was probably threatening to say that Bernie exercised control over Bambino during these transactions. This could quite easily have been a lie, but the threat of someone as knowledgeable as Gribkowsky saying it had to be taken seriously. Bernie could well have been the victim, it's one man's word against another.
It is of course quite possible that Bambino's trustees backed Bernie's judgment 100% and decided of their own free will to support their employee in whatever decision he took as CEO. ie. he didn't have to control them because they supported him to the hilt.