Who makes the claim? Surely such a claim is qualified by a certain brand and/or vintage. For example, there was a trend in the .22 Crosman barrels having oversized bores a few years ago.
All I can say is out of 50+ Chinese air rifles that have been through my hands in the last 5 years, I have seen no evidence that they have oversized bores. It has been a pretty even mix of mostly .177 and .22 and I have slugged a good many of them to look at how pellets engage the rifling. On the whole, large pellets show deep engagement and small pellets show shallow engagement.
In fact, I've noticed Lothar Walther barrels to have a comparatively looser fit until reaching the choke.
Conventional wisdom is that you need distinct engraving of the head to get good results but that is not what my testing showed. I've certainly had barrel/pellet combos that engrave deeply and shoot great but some of my best results have been with JSB pellets that barely show burnishing of the rifling around the head. As long as the pellet head is not so small as to permit it to tip in the bore, it has just as good a chance of shooting well as one that gets engraved.
Harry has written of similar observations in these posts: