After watching the video, I do not think an amp will help. If you listen carefully, you can tell the radio's amp is at full volume but the source volume is barely coming through. The noise I hear is like turning your volume to max while the music is paused. It sounds like when your amp's gain is set too high.
I think that radio is bad. Look at your settings to see if you can modify your source volume. Do not be afraid to move those eq settings. If it is external, I would say it is a wiring issue done at the shop.
Wait a minute, I take that back. If you use the RCA outs with an amp, you should be good. Bypassing the high speaker outputs would probably solve the issue. Before that I would test the RCA outputs. What if they have too little output; you would be back to square one.