Do Star Trek's Bussard collectors conflict with the deflectors?

In Star Trek, even at 'low' impulse speeds, colliding with a Very Tiny Object would be horribly damaging to the ship - see this NASA.org link which describes space shuttle windows being damaged by impact from paint flecks at high-velocity. To combat this, starships come equipped with deflector dishes; these are alleged to sweep the flight path of dust and debris and sometimes even provide some techno-magic Big Push to save the day against various objects of large mass - asteroids, the Borg, Paul Sorvino, and so on.

Finally, starships are also equipped with Bussard collectors. While these get very little on-screen explain time and even less emphasis on importance, these handy devices allow starships to scoop up particulates which the ship can use to 'refuel' - sort of a big giant Mr. Fusion.

But wait - the deflector dish is supposed to sweep particles aside, right? So in order for the collectors to even work, a ship would need to disengage the deflector dish, wouldn't it? Even at the low speeds we attain today, if a paint fleck moving at 18,000 mph can crack a window, what happens to a starship when it finds a particle moving at .25c?

Am I overlooking something (besides "it's only a show, just relax", or can these two technologies even exist in tandem?