You can easily use any arduino, including UNO, to burn an optiboot bootloader into a 8/168/328.
It just isn't done using avrdude from the IDE GUI which requires the UNO to act as a stk500 ISP programmer.
You will want to use the optiloader sketch instead.
The difference is the "arduino as an ISP" sketch allows avrdude to use the arduino as a standalone ISP programmer
device.
It turns your your Arduino into an ISP programmer that can burn anything in a chip.
optiloader, it is a sketch that runs on your arduino that only knows how to burn an optiboot bootloader
into a 8/168/328 chip. The bootloader is contained inside the sketch itself so it can burn the chip
on its own.
If all you need/want to do is burn an optiboot bootloader, the optiloader
sketch is probably a better/simpler solution
as there is no issue with autoreset since the sketch does everything.
Here is a link to the optiloader:
Another useful tool is the fusebytes sketch:
It will display lots of useful chip information on the serial port.
--- bill