I tend to think of hay as only a problem when it's the basis of a hamster's diet and they don't have other options. So Oxbow food isn't good because it's hay-based and a diet should really be based on seeds. However hay as a supplement or treat is fine and wild hamsters probably eat much more dried and fresh vegetation than pet ones do so they are capable of digesting it (maybe not as well as a horse or cow but reasonably well). It's good for hamsters' teeth, too.
