No, classical economic theory doesn't assume this. It derives this as a conclusion under some specific assumptions: demand and supply are elastic, many non-colluding buyers and sellers, good information and low transaction costs. The conclusion of classical economic theory is that under the circumstances I described above, prices will stabilize near a price P satisfying supply(P)=demand(P), where "near" is bounded by the size of transaction costs.

The paper under discussion is also classical economic theory, it just makes different assumptions: it assumes perfectly inelastic demand (i.e., users have no choice but to buy) and poor information/high transaction costs (buyers can only switch sellers infrequently and can't switch arbitrarily). It also assumes that sellers only copy the pricing strategies of others, and never come up with their own (e.g., no aggressive price competition).

It's not a "flaw" in classical economic theory, it's just applying classical economic theory to a new circumstance. It seems like it might be a good model for certain markets - mandatory insurance for example (auto collision insurance or health insurance in MA), display both demand inelasticity (you are legally obligated to buy) and comparison is difficult.