Fund buys stock at X and simultaneously solicits LPs at 1.2X (whether by straight mark-up or, more commonly, by adding management fees, research fees, expense reserves and carry.)
It’s why tenders have a few weeks between end of sellers submitting requests, confirmation of quantities and finally funding.
VCs usually raise a fund, i.e. a basket of commitments from LPs, before finding the investments. That means they negotiate the investment terms from a position of strength, commitments in hand.
With tenders, the investor starts by commiting to the issuer and then finds LPs. To the degree they have leverage, it's in their access to the issuer.
For the former, the fees are in exchange for risk. For the latter, they're for access.