You potentially have a case but you have a major issue that you have to overcome and the only way you'll know whether it can be overcome is by suing them and getting a copy of all of the work documents between the company and the repair man.
The issue here is that, as a general rule, most companies are not liable for the damages caused by independent contractors. While I have never seen a copy of the warranty which you purchased, almost all of that type of warranty also have a clause stating the warranty company isn't responsible for the problems caused by the repair people and by signing that original contract you agreed to that term.
However when you look at the terms of the relationships between some of the companies and the repair people they are independent contractor in "name only". By this I mean that the warantee company is actualy giving them almost all of the repair person's work, the company controls when they work, how they work, and all other details of their work.
If you can prove by either witness testimony or, more commonly, by the records of the company and repair man, that while they were called an independent contractor they were actually working more like an empoyee then you could win your case. If you can't prove that then you could lose against the warrantee company.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a 5 Star Positive Rating so I receive credit for my work. Of course, please feel free to ask any follow-up questions in this thread. I want to be sure all of your questions are answered.