Well for an example, it's not rocket science or heart surgery to fix a loose rubber grip, or other small cosmetic repair. It would appear that now you have to send your camera to Nikon and pay them to repair it, rather than buying the part from them and fixing it yourself (probably both cheaper and faster).
Not all camera repair jobs are technical, delicate procedures, and it is arguable that not many of them require any kind of specialized equipment either. Most Nikon repairs are probably simply replacing broken or malfunctioning parts and reassembling. Nobody's desoldering chips from boards, etc. they just replace the whole internal circuit board. Independent repair shops can do this just as well and likely faster than Nikon's big repair centers, and this can be important for those who depend on their gear. While I have not had any problems myself with Nikon's repair services, from reading the petition, it would seem that Nikon's own "quality control" could use some improvement as well.