"There is no evidence [except with frontline healthcare workers] that masks make any difference."
First, please be aware that the words "there is no evidence" do not mean "It isn't true". They mean "we don't know for sure". It meant the same when the WHO said, in early January, "there is no evidence for human-to-human transmission". It didn't mean there wasn't any, it just means it hadn't been documented and verified yet. Often, it also means "we're still looking for this evidence". It means "the scientific word is still out on this issue".
Secondly, please be aware that placebos work. Placebos don't have any ingredient that helps a patient recover, but patients who get prescriptions for them recover better than those who don't. Covid-19 is the cause of much anxiety, and sewing a mask has helped many people cope with that, and wearing a mask is
something we can do to not feel help less that may actually help (and won't hurt). So even if it turns out that wearing masks is nothing more than a placebo, it will likely have made many people more healthy and kept them more sane.
(Masks are also great as a placebo because, unlike bogus alternative medicine, it won't keep sick people from seeking a cure; and that mechanism is also why public messaging stresses that distacing is still very important even with masks.)
Third, disease transmissions is often "playing the odds", and the exposure to the germs is one factor that influences this. So if masks provide a mechanism that should, in theory, reduce the exposure of other people to the virus that an unknowingly infectious (infected asymptomatic) person exhales, then public wearing of masks will reduce public infection transmission by some amount. It won't affect the transmission that occurs in private settings.
Therefore, it stands to reason that this effect can be most easily seen in hospital settings, where a) the risk of transmission is high, b) the setting is public and everyone wears a mask. For frontline workers, the private unprotected risk is much lower than their public risk, so protection for public contacts will be much more noticable than if you look at the general population. But if we have evidence that this type of protection works in that setting, it stands to reason that it will also contribute in other public settings, even if the evidence for that is harder to come by (which typically means "it's very expensive to gather the amount and quality of data you'd need for a conclusive result").
So, what we learn from your quote is:
1) there is evidence that masks work in some settings
2) there is no evidence that they don't work in similar settings as well
The smart thing is to assume they probably do work in similar settings, and their use comes at very little cost compared to the benefits you could reap if they do work, even if just a little.
