Yes, it's the DVD Drive which is set to a particular region, and you usually get only 5 chances to change it, after which it will be locked on the last region selected.
I believe there are firmware modifications available on the web for some drives, but I wouldn't like to chance it with mine. There is also software available, which claims to allow playback of any region, such as DVD Region Free, but to be honest, I have found it to be not all that successful. The only sure fire way, if seemingly extravagant, is to get a second drive, and set one to R1 and one to R2.