They might mean that, but they'd still be wrong. Soldering is done around 75-100°C lower than temperatures where lead is anything other than melted in meaningful quantities. There is ingestion risk of lead residue on fingers (which is the reason why eating and smoking is prohibited around soldering stations), but very low inhalation risk.
Perhaps, but is generally accepted that as long as you aren’t soldering at ludicrous temperatures, the quantities are very small.
On the other hand, we keep finding deleterious effects from smaller and smaller lead exposure levels.
When I was taking electronics training, my soldering instructor told me most of the lead exposure was that people used to lick the tip of their soldering iron before starting heating it up, and this exposed them to lead. Now most people don't do that, but older solderers are a little... off, if you've ever met any. Rosin flux fumes are also bad and you should definitely be working under a fume hood if you do any significant amounts of soldering, even at home.
Well, we thought the same thing about aluminum [0].