It’s little bit more nuanced. Market failure in economics is rigorously defined as a situation where markets are not allocatively efficient (see Ledyard 2017). That is, technically speaking, market failure is an outcome, not some facet of market per se.
So technically speaking if informational asymmetry is present but market still yields efficient allocation, we would no longer consider it to still be market failure. I don’t have example about information asymmetry*, but for example, in presence of cost less Coasean bargaining absence of property rights or missing markets do not necessarily lead to market failure. I am sure there might be cases where this happens with informational asymmetry as well.
However, it is fair to say that typically asymmetric information leads to market failure.
This being said:
- I have seen many undergraduate texts to ignore this nuance and when discussing market failures just list informational asymmetry as a market failure, together with other examples.
- The commenter you refer to is incorrect in stating that informational asymmetry isn’t market failure if it is not fraud. Unless that commenter uses the word ‘fraud’ in extremely loose sense, i.e. keeping some information private also counts as fraud, the statement is not true. Moreover, under that broad definition every informational asymmetry would qualify as fraud.
*EDIT by OP:
For an example where information asymmetry does not lead to welfare loss, consider a 'lemon market' where the buyers have a higher valuation for both good cars and lemons than their sellers, and where the number/mass of buyers is larger than that of the sellers. In this scenario, all cars will be bought, and even though there is information asymmetry, the maximum possible surplus is generated.