While no expert (by any means) on the topic, that doesn't appear to make any sense. A gravitational slingshot maneuver is, IIRC, designed in such a way as to put the vehicle on the correct trajectory for the next leg of the journey. I may be wrong but I don't see how the planet's rotation would make any difference. Last night, I watched a program that talked a great deal about the Voyager missions. One of the missions (Voyager 2) flew past Jupiter and Saturn on to Uranus and Neptune. Now, Uranus's rotation is steeply inclined to the plane of the ecliptic (97.86 degrees). Voyager 2 had to slingshot around Uranus correctly to fly on to Neptune. If the planet's rotation seriously affected the slingshot maneuver, it seems unlikely they could've aligned the trajectory correctly. Both planets' orbits are almost inline with the plane of the ecliptic (less than 2 degrees of inclination) so it seems likely to me that Voyager had to fly a trajectory pretty close to the plane to reach the next planet. Uranus's unusual rotation would - it seems to me - have thrown the spacecraft north or south of the ecliptic if rotation was a factor. I don't think I'm explaining this well.

Here's a link to a NASA Gravity Assist Primer. I just skimmed it but I didn't see any reference to the planet rotating on its axis, just a reference to the planet's rotation around the Sun. There a link on the page to a 1.5 hour (in 4 parts) video on Trajectory Design and Gravity Assist. I don't have time to watch it now but it might be interesting.