That never made sense to me either. The best I could come up with was that the shuttle had a fuel synthesizer that couldn't be used until Scotty powered it with a phaser.
The dialogue above doesn't outright contradict that, but it only works if you assume Spock and Scotty are leaving out half the details.
In Farscape, the Pulse Pistols were powered by oil. Similarly, the EU indicates that Star Wars hand weapons are likewise powered by a gas.