In short, it's true. if you have an AppleCare Protection Plan that is currently in-force for a Mac that you own, your Time Capsule is covered under that agreement. In fact, there is no need for the Time Capsule to be on the same receipt as the computer you purchased. As long as the Time Capsule is owned by you and "in use" along with the covered Mac system, it is covered along with the product for which you have an existing AppleCare Protection Plan.
Of course, this does not cover any damage you inflict on the Time Capsule, and it must not be hacked or used in any way other than it was intended. In other words, don't use your Time Capsule as a doorstop and expect to get AppleCare coverage on it when it breaks.
In addition to the Time Capsule, this "in use" coverage extends to the following products:
- AirPort Extreme Card
- AirPort Express
- AirPort Extreme Base Station
- Apple-branded DVI to ADC display adapter
- Apple RAM modules
- MacBook Air SuperDrive
All of the above is contained within the terms and conditions of the AppleCare Protection Plan for North America. In addition to those actual terms, an Apple Genius I spoke with said that coverage also typically extends to Apple-branded hardware on the same receipt as the covered computer purchase, and in general he and his colleagues endeavor to extend the best courtesy they can to their customers when the situation permits. So you may, in fact, receive coverage better than the terms within the agreement itself if you are pleasant, don't yell at the nice Geniuses and say "pretty please." Complimenting their shoes is always a nice touch. They also like chocolate.
If you'd like to check to see what agreements are current, you can click here to check them out, see when they expire, and read the terms and conditions yourself. If your agreement is not registered or is not listed under your Apple ID, you can check by agreement number and computer serial number. Also, if you are not in North America, you can read the terms specific to your agreement here -- many European countries have stronger consumer protections than the US does, and longer warranties may be standard where you live.