Actually, if we're going to be strictly "textual", I'm not sure what you say is in the Bible, either.
We know 1) Judas was a thief and 2) he betrayed Jesus and received 30 pieces of silver in return. It's an assumption to allege that #1 led to #2.
In fact, if you read the sequence in which Luke describes the events....
"And Satan entered into Judas, who was surnamed Iscariot, one of the twelve. [4] And he went, and discoursed with the chief priests and the magistrates, how he might betray him to them. [5] And they were glad, and covenanted to give him money. "
Luke 22:3-5
....it appears as if Judas' primary interest was in betraying Jesus. The priests were glad and subsequently agreed to give him money.
And I could accept your explanation as being derived from the text ... but I think we would both agree ... that is nowhere near what the pope said.