well if you read Matthew 4. Jesus followed the invitation of the Spirit to many places. It would not make sense for Jesus to follow Satan for some period of time for sake of preaching to Satan.
So Jesus was tempted on what the Spirit had to offer him. and Jesus kept on following the Spirit for possible offer that does not contradict to Yhwh's Law. Til..
In the end, Jesus figured out the Spirit was eventually Satan when the Spirit made a statement "Bow down and Worship me"
If the Spirit tempted with something that does not contradict to the Law of Yhwh. The version of Jesus portrayed in those Greek books may have accepted the offer.