Whether it can in principle, versus whether it does in reality are of course two very different things.
Even that might not be so bad, if a huge chunk of the audience did not consider it their moral duty to shut off their brain.
Yes, what a free market does is match supply and demand via price signals. It is the aforementioned Econ 101, using mechanisms discussed in Econ 101, which are all mostly math and border on physics. What people don't like is that it does so entirely a-morally (not im-morally as some would like you to think, but actually a-morally, with no particular regard for human morals), so you will sometimes not like how it does it (thus, price gouging laws during emergencies; the free market is trying to balance a sudden supply shock with skyrocketing prices, and we don't like that), and sometimes we have to intervene to prevent it from amorally doing something we don't want to happen at all (hence the need to sometimes straight-up ban things; a free market will efficiently price slaves, drugs, or hit jobs perfectly amorally), but in the normal case, what a free market does is match supply to demand with price signals, regardless of whether we "like" the result or not. It is sufficiently efficient at this that a long-term failure to match up supply & demand is extremely strong evidence (though not quite 100% proof) that there is not a free market where the mismatch is occurring; something's fiddling with the prices outside of normal supply and demand mechanisms. (An interesting example in the other direction is that our War On Drugs has been rather ineffective, as can be shown by the fact that supply and demand are often quite well matched up via pricing; despite our best efforts there still is a fairly free market in drugs!)
