I can't see any reason why you wouldn't be able to go from 10.1 > 10.3... Maybe if they made some kind of upgrade-only disk available for a lower price you would need to already have 10.2.
But that aside, if you pay the full OS price (ie. $129, or around £100 over here) you get the full OS, which you should then be able to install on any compatible Mac, no matter what OS version it already has.