If you took it somewhere else and paid them for fixing the problem without first going back to the original shop and giving them a chance to correct it, it'll be a much harder case to prove.
They can still argue that the part they fixed was part of the problem and who's to say it is not unless it is blatantly obvious like say they replaced a part in the rear end of you truck and the problem was found in the front end and so far away from the work they originally did .
Even then they can still claim the 2 places were connected.
Case in point, I just had starter issues. The place I took my truck to replace the starter put in a new starter.
The new starter made a lot of noise, pissed me off and generally caused me to have a deep distrust of the quality of work they do.
After numerous weeks of them diagnosing everything else including my ignition, remote start etc. I got fed up and took it to GM.
GM said it was indeed the starter although they also had to fix other parts which got messed up due to the bad starter install.
Instead of just having GM fix it at even more money for me, I decided with the advise of others on the forums to take it back to them with the paperwork from the dealer stating the problem was the starter.
At this point the first shop replaced the starter and reimbursed me for the cost of the work GM did as well as their diagnostics fees.
That being said every situation is unique and can be handled differently depending on the circumstances.