The whole reason the House distrusts the Senate is that the Senate has a filibuster, which has meant that every single Democrat must hold together in the fact of GOP obstructionism in order to pass anything substantial. To pass a reconciliation patch, the Senate can afford to lose nine Democrats, which makes it a piece of cake. Which is to say, the House is acting irrationally. It needs to pass the Senate bill and trust that 50 Democrats can be found to carry out a verbal agreement.
The flip side, of course, is that the irrational distrust of the Senate is part of what gives the House leverage here. In a negotiation where both sides have a strong incentive to compromise but the parameters of agreement are wide, the side that can more credibly threaten to walk away has an advantage -- which is to say, the crazy man wins.