Carl Icahn is a driving force in persuading HP (HPQ) to merge with Xerox (XRX), according to HP, the larger of the two printer makers. He’s also one reason the HP board can continue to say no in the face of Xerox’s $35 billion hostile bid. Icahn’s pursuit of a tie-up is rational, but his self-interest and influence over Xerox obscure a potentially worthwhile deal.

HP’s detailed blow-by-blow, published on Thursday in a preliminary version of materials for its annual shareholder meeting, says Icahn proposed HP should buy Xerox as early as August 2019, two weeks before Xerox Chief Executive John Visentin suggested something similar. Icahn even hinted he could buy HP. Later, he proposed a price at which HP might make a bid for Xerox. Xerox says HP has “misrepresented” the interactions, without giving details.

Two things are clear. First, because Icahn owns shares in both companies he benefits from a deal, regardless of who buys whom. No wonder: Xerox thinks the annual cost savings from a combination could be $2 billion. Tax and capitalize that and it’s worth around $16 billion in today’s money, almost half the combined market capitalizations of the two before news of a possible merger became public.

Second, Icahn’s influence over Xerox is more significant than his 11% stake would suggest. He proposed Visentin as chief executive and nominated most of its board directors. HP says presentations it received separately from Icahn and Xerox contained slides that were “substantially identical.” That creates the impression that the deal is Icahn’s initiative as much as Xerox’s.

HP’s board has been aggressive in its defense, installing a so-called poison pill and refusing to give Xerox non-public information unless the other company does so first. That’s a shame, because a combination has merits. Substantial cost savings would provide some buffer for the revenue declines in each company’s core business. HP recently said it was “reaching out” to Xerox, which is encouraging.

Yet it would be easier to criticize HP’s stubbornness were it not for Icahn’s intrusions. The irascible investor has a record of pursuing short-term gain partly through bluster, and his position on both sides gives him a different interest than investors on one or the other. If he really wants a deal to happen, he’d be better off keeping a low profile.