Agreed that velocity is an important component, but I hope we can also agree that dumping large amounts of money into the economy (ultra low rates and QE) will result in price rises.

At the whole economy level, I'd suggest that supply and demand don't really cause inflation - at least, not the kind of disfunctional inflation that we should guard agains. For example, if the supply of bread is reduced, then necessarily people will eat less bread (and price signalling will ensure that it is the poor that eat less bread). So long as this does not trigger e.g. a wage price spiral or other pathological effect, then this is 'fine'.