Yet, at some point, did lords mess about with the titles that their vassals had (or could claim to have)?
Certainly, the pope did this. The Republic of Florence, became the Duchy of Florence, when Clement VII appointed Alessandro de'Medici duke. It then became the Grand Duchy of Tuscany, when Pope Pius V declared Cosimo I Grand Duke. This title was greater than all those in Italy (barring Naples/Sicily).
Popes certainly crowned emperors, and while it's not as simple as the Pope picks somebody, there is the sense that there existed an authority which could define, or perhaps approve, titles.