It is a shame that things like circuit boards on home devices are not designed to be more repairable, but that's how it is at the moment, they are produced in bulk and making them repairable would, at least in the short term, increase the initial production cost. In the longer term, writing now at a time when the USA are about to ratify Paris global emissions treaty, I think it's likely that governments will legislate "maintainability/repairability" and a "right to repair" as a required standard alongside existing safety, energy efficiency, toxicity standards etc. to reduce overall electronic waste. I believe "right to repair" already exists in limited cases in parts of the USA e.g. certain car manufacturers in certain states being required to publish repair manuals?)
So that being the case, currently nobody will resolder a circuit board, sounds like the first guy is an idiot or a salesman in overalls, and the second company are either being cautious (don't want to order a $400 replacement board without investigating, then find customer was wrong so can't sell that board to customer) or are quite happy to bump up the repair cost with an additional call out fee.
If the second repair does go smoothly I'd be asking the second company if they would reduce or waive the second call out fee (they may say yes, no harm in asking politely), and I'd be tempted to report the first company to the relevant government department for deliberately misleading you (Trading Standards in the UK) i.e. if one repair company can get the part why can't another, it would appear they deliberately mislead you to try to increase their sales, which at least in the UK is against the law as companies are required to provide a "reasonable" service. If the government department gets multiple complaints about the same company I'd like to think they would take some action.