A simple movement from an independent should be able to be serviced by any competent watchmaker. But something more complex might be difficult even with the schematics and technical instructions of how to do it. Furthermore, servicers sometimes damage things of their own and will need to craft parts. Now... If it were really that easy... Then why are we putting these special independents on a pedestal.
Furthermore, some collectors couldn't tell a good service from a bad service. Save from an obvious scratch on the mainplate or something causing the watch to be unreliable or inoperable, most collectors are actually quite unaware about watchmaking. Others are fanatics, they will loupe everything they can see and inspect it thoroughly. Most people do not know what they do not know.