It can be done.
There are two parts to the Arduino software: the IDE and the libraries. The IDE can be configured to work with any AVR processor. The libraries are really designed to work with a processor that has more Flash and SRAM than the ATtiny13.
There are folks who have mated Arduino to ATtiny13 and written to tell the tale...
http://accrochages.drone.ws/en/node/38
http://www.google.com/search?q=attiny13+arduino
If your uncle (or you) really wants to use the Arduino libraries he is far better off replacing the ATtiny13 with a "bigger" processor. The ATtiny85 (and "up") is a good choice.
If your uncle (or you) doesn't mind directly manipulating registers then the ATtiny13 with the Arduino IDE are a good choice.