No. Europa and all the moons closer to Jupiter than it do in fact occasionally travel backwards in relation to their orbit around the Sun. This is also true of Dione and all the moons of Saturn lower than it, all the inner moons of Uranus, and all the regular moons of Neptune.

The gas giants are much more massive than earth, while also being much further away, and many of their moons orbit closer to them. This all combined makes some of their moons pulled more strongly by them than they are pulled by the sun.