Today I got some extra Atmega168A-PU's. I already had some PA-PU's. I know the signature of the regular 168 devices are different and I knew that I had to change "something" on order to get the bootloader up and running. The funny thing is that I might have gotten it to work some time ago. The bootloader said to be burnt when altering the board.txt file so it would load the m168p file instead of the non-p. However, I was fully sure that the USBTinyISP could put programs on the IC's from within the Arduino Environment. However, when I disconnected the USBTinyISP, connected the Arduino board and selected the corresponding com-port, all worked well!
So, I fixed the problem, which wasn't there after all.
As for the 328P devices, the Uno uses those too so when I selected that board, all worked too.