The house only passed that bill because Trump called Paul Ryan personally and said he would veto the bipartisan budget that was on the table and passed by the Senate. This is no fiction, it is Trump's shutdown
Everyone knows Trump's refusing to sign a budget without wall funding, that's no secret.
The part you left out is that the Democrats blocked a bill with wall funding, even before they took over the House. Trump never "had a perfectly good budget on his desk, written by his allies and passed by Republicans".
Both parties put this issue ahead of the continued operation of the government and both are responsible for the shutdown.