This rationale suggests that PLAN didn't have any frigates until 2005, despite building generations of ships that were labelled as such by themselves and others.
Of course PLAN refers to 056 as a 'frigate' and most of us are comfortable using the external designation 'corvette' to emphasise the significant differences between it and the 054 series, so PLAN's internal designations are not necessarily authoritative.
The question is whether it is appropriate to 'back-date' classifications to reflect modern standards and subsequent developments. I don't think it is, not only because doing so opens an enormous can of worms for no clear benefit (a lot of designs around the world would be up for re-evaluation), but because a nation's classification structure often has implications for the future, even if the vessels within those classifications evolve significantly over time. In China's case, the term "frigate" has been used to describe second-line vessels that are smaller than PLAN's first-line combatants, destroyers, but significantly larger than third-line patrol boats, missile craft, etc. Even if their capabilities more closely resemble today's third-line vessels (i.e. the 056 series), as formerly second-line warships, I expect PLAN's current 053s to be replaced with new second-line warships -- i.e. vessels of the 054 series (or subsequent follow-on). And as such it is reasonable to keep the 053s in that category in the meantime, almost as a "watch this space" marker.