Most likely that they are usibg the gravity assists to decrease the orbit (e.g. slow down) not to increase the speed. As your orbit gets more and more elliptical, your closest point to the celestial body gets closer and your actual speed relative to the celestial body increases dramatically.

It sounds contradictory, but think of that in this way: you have an incredible amount of energy stored in potential energy relative to sun and by decreasing your orbit you convert this to kinetic energy.

Think about falling into the sun from several billion kilometers, but just missing it slightly because you still have a bit of horizontal momentum left.

The opposite, actually. Increasing speed is the very thing that brings it closer to the Sun.

To clarify a bit... The gravity assists from Venus actually decrease the probes instantaneous speed, which allows it to fall closer to the Sun. The act of falling towards the Sun is what generates speed, with more speed being generated during closer approaches.