There are actually thousands of these machines out there.
www.cnczone.com is a very large forum/site for hobbiests that make their own CNC machines out of a huge variety of materials. Kick around over there and you will see the Bridgeport that I converted to CNC.
It is possible to make your own CNC that can hold very tight tolerances but obviously it depends on the design and components used. I have seen several machines made from gas pipe and threaded rod that perform well enough for what they were intended for. There are also some pretty incredible machines on that site - homebuilt.
Getting into +- 0.015" is fairly easy. Getting to +-0.003" is a bit tougher, while holding "tight" tolerances is a completely different realm. It also depends on what it will be doing. Some machines are built just to drill PCBs, some are built to route wood and wood products and others are built for milling aluminum and steel. The designs and materials used mirror their intended use.
It is amazing what can be done with commonly available materials like threaded rod and gas pipe! Some of these homebuilt machines are very impressive. For example - the guy that built this wooden machine could mount a plasma torch on it and cut pretty accurate parts for a slightly smaller steel version then use higher accuracy parts to make a more accurate, more robust machine.
Scott
