had one like this last year, complete nightmare, so I sympathise. They seemed to believe the 'customer is always right' maxim should always apply, and I shouldn't have the temerity to point out the errors in their logic.
Still out of pocket by about £350 for that job (solar water heating repair) that they'd specifically promised there would be no problem with payment for, after we'd been in dispute about previous works for several months and then settled. Apparently we should have continued to work on the 2nd system despite them refusing to pay us for our previous works, and even attempting to charge us for call out and maintenance costs for a swimming pool unit that it turned out hadn't had a service for about 8 years, and had a whole series of documented underlying faults as a result that had nowt to do with us.
I said to leave it over Christmas, but we wanted paying by the end of January... trying to work out if it's really worth my while attempting to chase that debt, but it really grates the amount of staff time we put into them last year, I must be at least a grand down at the moment all in.
I even requested in the summer that they find someone else to service their SWH system, and tried pointing out that we were actually under no obligation to carry out any further works for them if we didn't want to, but they kept insisting they didn't want anyone else to do the work, and like a sucker I agreed once the previous dispute was settled.
Hope you get your situation sorted out - it might be worth emailing the other company to just put your side of the situation to them to set the record straight and save them potentially bad mouthing you on the say so of this customer.
