I am reserving judgement about the issue but would like to point out two additional non-canon sources for the V'ger-Borg connection:
Star Trek: Legacy
represented V'ger as a mal-programmed machine that built Borg to assimilate all universal knowledge. The carbon-based Borg, however, rebelled.
Star Trek Online
does not reference any specific origin story but the Borg have copied the design, which conceivably they could've taken from Starfleet databases. (Remember how Starfleet employs the Dauntless
-class in a possible future?)