Such high ratings are usual for transmitting antenna tuners. In this case it may be over rated just for security. Take care with old tube radios because they used to have a "hot" chassis. That is the chassis is connected directly to mains.
The capacitor blocks harmful voltages so you dont get a shock if you touch the FM antenna. I guess that 1000v is ok.
I dont think that the problem is caused by the capacitors. If the two capacitors are in parallel the radio will receive normally with just one of them.
If you hear no noise at the fm band then certainly the problem is somewhere else. You can test by connecting a length of insulated wire as a temporary antenna bypassing the capacitors. take care though the wire could be "hot" is not the final solution.