why would he call up the mechanic who did the job? He's the one who let him go with his price and he's an owner. Of course if he talked to him, after getting in shit from his partner he's going to change his tune.
Some mechanics are honest, they have a pricing book but if it is shorter in time, they don't charge the time.
If the mechanic owner did the work and only invoiced for 2 hrs, then its his problem. Sure he was quoted 3 hrs by another owner but another person of authority charged less and let him go.
I've been laying under cars since I was 8 years old. I have motor oil in my blood. I've known scores of mechanics - from dealers, to the neighbourhood type, to the cash out of their garage at home types.
They live and die by the flat rate system. Even the dealer mechanics get paid flat rate (not by the hour).
I look at it from the point of view that the second guy made a mistake and the OP knew it was not what he was quoted. You don't penalize a guy for an honest mistake. If the OP calls up the second guy at the shop and he says, "don't worry about it, I quoted you 2 hours, we're square", then that's it. But if the second guy changes his tune (as you so aptly put it), and says he made a mistake, then he made a mistake and you pay the man.
To do otherwise is not correct, despite what you and others may think.
I've been in situations very similar to the above where a mistake was made in invoicing work done and the mistake was realized and I was petitioned to make sure that I realized that there was an error and I stood by my word. You don't penalize a guy for a mistake. I've even been in situations where a mistake was made in the QUOTE after I carried the subcontractor's price and he realized his mistake and told me, "I made a mistake" and I've paid what should have been the correct price. I've seen clients pay corrected invoices for hundreds of thousands of dollars because a quote slipped a zero. I won't get into exact details because I will out myself, but I'm thinking of one instance where an item of work in a huge quote slipped a zero. Instead of being $110,000.00, the firm in question signed and sealed for $11,000. (It was a multi million dollar contract) But it was a hundred THOUSAND dollar typo. They appealed to me and the owner that they made an honest mistake and they had to correct it and upon reflection, both the owner and me agreed that it was a mistake and the mistake was realized and that since a service was rendered, it was proper to pay the correct price. There is actually legal precident for this. (Sorry, I'm not a lawyer, but it was explained to me.)
The only mistake the shop in question has made is that they should have PHONED the OP, never mind texting him. Texts are for kids. If you want to be serious, at the very least you get on the phoine.