It's a really weird claim that they don't exist when the first search result for "airless bike" is an amazon link with a large selection of airless mountain bike tires. Is he using a really restrictive definition of mountain bike tires? I looked into this when I moved somewhere I was getting constant tube punctures, but the general consensus seemed to be that they all just suck for various reasons. I ended up going with tire guards plus bike tubes with sealant, this combo seems to work very well, only need to replace the tubes once or twice a year despite multiple thorns getting stuck in the tires every day that would otherwise cause a flat.