Another dissatisfied home warranty customer - how novel. How I hate home warranty plans - lots of promises, but no chance of fair delivery because they are priced competitively well below what they should be to actually have a chance of making a profit without cheating the customer - one of the main scams out there, in my opinion. More on that if you are interested in prior questions - put the phrase - home warranty - into the Ask box for links if interested.
You said the first one said you have an repairable leak in the handler and it needs to be replaced - I presume you meant an UNREPAIRABLE leak, like a leaking evaporator coil probably. Normally, one would replace the coil like the second guy said, not the entire handler for this - unless a replacement coil cannot be found to match the unit.
If this is such tight clearance that he has to be laying down to work on the unit, then yes a stand or a rafter-hung come-along might be needed - but that is HIS problem, not something you should have to do. His demand is equivalent to a mobile mechanic working on a low-slung car saying you have to provide a lift or elevated platform to lift the car up high enough to work on - that is part of HIS job to come up with. A slab of plywood (or one top and one bottom if exposed attic floor joists) and a couple of 2x4's nailed or screwed together should do the job - the coil is not that heavy (maybe 50 pounds max for a residential unit, more likely 20 pounds or less in most cases). I would guess that, given dimensions from the tech up front and a description or photo of the worksite, a handyman could probably do it in one visit for about $150-200.
I have also seen HVAC guys use a plastic tool tote for this and to carry tools and parts too - couple of 2x4's under it to straddle joists if not solid floored attic, tote with its lid snapped on, scrap of plywood on top to distribute the weight and act as a work platform.
This is a common problem with warranty company techs - they are getting paid a flat rate for the job in most or all cases, and generally well below market value, so any additional effort comes out of their pocket so they charge add-ons like that, or try to tack on additional upsells (commonly wiothout the warranty company even knowing about it) to increase their take. And like you said, if the second guy had not heard about the stand issue he would probably have gone ahead without it.
My position (though I might be more obnoxious than you with warranty people) is "you warrantied it in its existing condition - YOU pay for whatever it takes to repair it". And remember - while the tech is the guy talking to you, the warranty company is who you have the contract with, and any arguments or non-performance issues that come up should be handled with them, not the tech unless he is pretty agreeable. Except with a few warranty issuing companies like A&E and Sears (and even in that case many times), the tech is almost always NOT their employee, he is a subcontractor. And with warranty companies firm insistence that they abide by their contract, and if necessary (the "nuclear" option) asides about filing a consumer protection agency or consumer fraud complaint against their company commonly get results, because that sort of thing not only upsets management but the rep you are talking with gets dinged seriously - or fired - if that comes from one of their cases.
