The possible Laverda connection came from comments made by Piero Laverda (the surviving brother of the original Laverda motorcycle dynasty). Piero said that when Aprilia bought the Laverda factory, they didn’t buy the 3-Cylinder concept as it seems they thought it had no future and they were not willing to pay for it. Although oddly enough, they went on to design their own in-line 990cc triple for MotoGP, which they called the “RS Cube”.
Anyway, the story goes that some of the personnel from the Laverda design team for the 3-cylinder engine had connections with Benelli, and to quote Piero: "You could argue that the Benelli Engine is based on the concept of the engine that was under construction in the 90's at Laverda."
So, I don't know whether Laverda's design drawings found their way to Benelli, but Piero seems to indicate that there was some kind of technology transfer.
On the other hand, it may all be rumour and wild speculation. Next time I see Piero, I’ll ask him.