The VC likely already has ownership, and a board seat - public companies are susceptible to activist-investors and hostile bids: outsiders who hold little/no stake, but an outsized influence.
Neither of which would be relevant in the Stripe case, because if Stripe IPO's they'll release a negligible number of shares. It'd be impossible for either group to amass a substantial number of shares.
A low liquidity IPO would likely result in a massive share price increase: the number of interested buyers would vastly outnumber the number of shares available.