This is not true. You're right that it would quite slow, but end-of-mission options were investigated that would have sent Cassini all the way to Uranus or Neptune:
Titan specifically (none of the other moons are big enough to have any significant effect). Even if you're aware of that, it's a pretty surprising result, since it took so much more delta-v to capture into Saturnian orbit than it would to escape (mostly because we wanted to fly Cassini to Saturn and capture it into orbit in a reasonable amount of time; the trajectories that could've been used to escape from Saturn were quite slow).
noted that it would've been possible to escape (in the year 2014) to Jupiter (2021), then use gravity assists to also visit Uranus (2029) and Neptune (2061), or use Jupiter or Uranus to escape the solar system. Cassini also could've used any of Io/Europa/Ganymeda/Callisto's gravity to be captured in orbit around Jupiter, or entered into orbit around Neptune using Triton. I assume the main reason none of these options were chosen was that, with limited fuel remaining and the spacecraft not expected to remain operational forever, it was seen as more valuable just to stay at Saturn until end of mission (as well as pick up a bit more science diving the probe into the atmosphere).
So practically speaking, leaving Saturn once it got there was never really an option.
Now, if you could find a way to scoop up some ring material or gas from the planet to refuel...