I want to point out here that there is no such thing as a "certainty" in science. When we state something is a "fact", there is always the possibility, however remote, that it could be wrong.
What we do know is the effects of nicotine on the human body, the effects of PG and VG on the lungs, and the effects of flavorings when ingested. We know that none of these are carcinogenic (reducing the probability of causing lung cancer at some later date to near zero), and that the amounts of PG and VG we use have no long-term damaging effects on the lungs. We're still a little shaky on the long-term effects of nicotine, but we're sorting that out fast, and we haven't found any major concerns yet. The great unknown is the effect of these flavorings - however, given that we can ingest them it is unlikely that these will pose very serious problems when inhaled.
Now to your point - how can we predict that these will save lives? What I've illustrated so far is that we expect no more than minor health concerns from long-term use, based on what we know for sure. Now there still remains the possibility that a few lives will be lost when millions use these long-term - that is an expected probability. However, we also know that smoking kills 480,000 people per year in this country alone, and when adjusted to expected population increases over time we expect to lose about a billion people within the next century.
The reason that they can make the claim that APV's will save millions of lives is that they have been proven to be an adequate replacement for smoking. When you compare the expected death rates from vaping with the expected death rates from smoking, it makes perfect sense to say that if even half of the smoking population switches to vaping, millions of lives will be saved.
Of course there is no absolute certainty, but that does not mean that we can't make a persuasive argument based on the knowledge we currently have.