Yes, beer in the lines can become oxidized. This happens fairly easily in vinyl tubing, not so bad in barrier tubing. The answer to this is to clean the lines regularly, and to sell enough of your beer so that it doesn't stay in the lines long enough to become oxidized.
You might also want to check and see what type of dispense gas he is using. In some older accounts I have found both straight air from an air-compressor being used, or a CO2/ air blend for longer draw systems. Needless to say, this will oxidize the beer in the keg quickly, over a matter of days. At one place, since the Bud and Coors kegs were never around long enough to get oxidized, due to his cheap beer specials, the owner seemed to think that it was a problem more with my beer than with his draft system. He wanted us to "pay for the improvements that only our beer needed" so we declined to do business with him anymore.