Logic isn’t fact

Logic is a process, not a fact. The simplest definition I have seen is: Logic is the art of non-contradictory identification.

Dr. Bo's Criteria for Logical Fallacies:

It must be an error in reasoning not a factual error.
It must be commonly applied to an argument either in the form of the argument or in the interpretation of the argument.
It must be deceptive in that it often fools the average adult.

It's an ambiguous statement.

You'd need to ask what they mean, and prise an argument out of them.

If their reasoning is as follows:

P1) My argument contains a logical fallacy, however

P2) Logic is not fact, therefore

C) The aforementioned objection is meaningless

Then we have a standard non sequitur. Logic is the study of inferences, not 'truth' (except for logical truths, and even then, those are different kinds of 'truth'). However, an argument containing a fallacy is not logically valid, so pointing it out is worthwhile in a debate context.

If their reasoning is:

P1) My argument contains a logical fallacy, however,

P2) Arguments containing fallacies may have true conclusions, therefore

C) The aforementioned objection does not prove my argument false

Then this is a valid - and true - point (see the argument from fallacy). However, it still fails to deal with the fact that the argument is flawed. Furthermore, person 2 never said anything about the argument being false, they simply said it was invalid - so person 3's response could be considered a red herring.

TL;DR: More context. Ask what they (person 3) mean!