If the scratch is truly deeper than the clear coat, then no, it can not just be polished out. What I might suggest (take this advice with a grain of salt proportional to your comfort level :wink: ) is try the touch up paint method first, if it works, awesome, you just saved $500, if not, it's going to be the same price to have the pros do it again for you. Here are the steps for touch up if you are interested (please don't hold me responsible for any mistakes, it's best to try this out in a hidden area first):
Wash the damaged area, then clean with a wax remover (which you can get at your auto parts store, often sold as a paint prep cloth)
sand the scratch with 600 grit wet / dry sand paper (also available at auto parts store) you want to get the edges of the paint around the scratch as well, be sure to remove any paint that isn't well bonded to the surface. A little circle of 600 grit glued to a pencil eraser works well for this. If the scratch has exposed metal (doesn't sound like it in your case) be sure to remove any rust.
clean area again with alcohol.
(If the scratch has exposed bare metal you are going to want to hit it with some primer. If you get a spray can of it, spray it into a cup and use a toothpick or end of a paper match and just touch the match to the metal, if there is a glob of paint on your applicator, scrape it off. Just touch the applicator to the chip, the primer should coat the surface with out much help, you are going for a *THIN* coat) Let the primer dry for at least 2 hours, then apply another *THIN* coat, again. Let dry for 2 hours.
Shake your touch up paint well!
If the paint seems to thick to spread well, you might want to cut it down with some acetone (a few drops) to thin it down (keep the acetone away from your car, it's a very effective solvent

)
Don't use the brush or pen that came with the touch up paint, use either a toothpick, paper match, or a #000 sable brush from an art / hobby store
Avoid the temptation to fill the chip / scratch in all with one go, all you should be doing is touching the toothpick to the chip and the paint should flow to the edges of the chip. Too little paint is good, too much is a bummer. Let the first coat dry, if it is still a little divot, repeat with more coats as needed, go slow and be patient, it's a lot easier to build up than to take down. By the way, this should not be done in direct sunlight.
The paint application is complete when the new paint bulges upward slightly (we are talking a fraction of a millimeter) Let the paint dry for a week
Attach 2000 grit wet / dry paper to a small block and very lightly! "plane down" the high spot in the paint with water flowing over the surface to carry away any grit. Try to sand in one direction, back to front of the car until the new and existing paints are blended. Wash the car, then use polishing compound to remove the scratches left by the 2000 grit sandpaper (again, don't go in circles, just a back and forth motion) Don't go crazy with the polishing compound, you don't want to wear through all of your labor. Finish up with a nice glaze (try Maguire’s or 3M hand glaze)
When applying glaze, apply with a soft cotton cloth or applicator pad, don't just squirt it on the car, use a front to back motion, not circles as that can cause swirl marks. Buff out with a soft cotton cloth, if it all looks good, finish it up with a quality hard wax and you are good to go! As a tip for the wax, when applying, try using your fingers instead of a cloth, this way you can feel when the wax is worked in, and you can also feel if you have hit some grit that will scratch your finish.
Hope all goes well!