I am not sure if the bit about eating a shifter is entirely accurate. There might be something to it however the scenario is still weird. We know there are classifications to titans and generally titans of a certain height have a certain look. Then we have shifters are normal titans. Normal titans are generally to some degree deformed and have, well, stupid or creepy looking faces. In turn shifters pretty much seem to stick to the type corresponding to their height however there is more to it. They do not have the same stupid looking faces and rather than being deformed or apparently overweight they seem fit, slick, even muscular. Ymir is no exception, she is agile, strong, muscular and her face different from other titans of her type. We saw a small flashback of when she ate that kid, she was not like the other shifters. She was probably like a rampant transformed eren except that her rampancy lasted for 60 years.
http://www.mangareader.net/shingeki-no-kyojin/40/44
Also, maybe I am mistake but didn't ymir say she stole her titan powers? If she stole them then she was not quite like regular titans to begin with. Maybe eating their friend had something to do with ymir awakening but it is not necessarily the source of her being a shifter. Maybe eating someone was simply enough of a shock to wake her.