I've experienced the situation you described. After the fitters left, I noticed some cuts across the top of the carpet, parallel to the edges around the fireplace. It was obvious to me that the fitters had folded the edges back and cut through the into the top of the middle.
When I complained to the shop (after talking to Trading Standards about the grey nature of the contract(s)), they sent someone round who looked at the cuts and said there must have been a fault in the carpet itself. He said something like, "Don't worry, we'll get it replaced with a new piece," ordered a new piece, and sent the same fitters around with it. The replacement had similar cuts, but in different places. He came round again and couldn't believe the factory had sent another defective roll of carpet! The third time, they did it very carefully.
When I wanted new carpet in another room, I went to a different carpet shop and specifically asked about the fitting contract. *That* salesman said something like, "We use our own fitters and you pay us for the materials *and* installation. We're not dodgy." The fitters were competent that time.