Actually the quality now varies almost as widely as steel and aluminium. There are some quite inexpensive titanium frames on the market, but they tend to use lower grades of material than the 3 percent aluminium, 2.5 per cent vanadium alloy that's used by quality builders such as Merlin and Litespeed. If not, you might be in trouble Gary Helfrich will be along in a moment to claim that this is bollocks and that titanium is only slightly harder to weld than steel and much easier than aluminium. Also you're confusing welding with bonding, two totally different processes. Sorry, but this is just plain bollocks.
Bike frames are damn nearly perfectly rigid in the vertical plane, whatever they are built from.
I suspect it's another piece of bike culture folk bollocks. Carbon tubes are usually molded, but are then joined into frames by bonding into lugs. Trek, Giant use this process and they must account of the majority of carbon frames out there. Some people can convince themselves of anything in order to pander to their prejudices. Which isn't to say that carbon frames aren't flexible, no doubt some are, but this is just more repetition of 'lots of people say this so it must be true' bike folklore bollocks.