There are some situations where an object will use a Disposable resource whose useful lifetime exceeds that of the new object that used it. There will be other situations where one will expect to hand off an object to an entity which knows nothing about any disposable items within it. Some types of object may find themselves used in both scenarios.
Consider a hypothetical IDisposable SoundPlayer type which will play an IDisposable SoundSource object and then dispose of itself when it's done. It's easy to imagine situations where one would want to be able to load a SoundSource once, play it multiple times, and then manually dispose of it afterward. It's also easy to imagine situations where one would want to load a SoundSource object and then "fire and forget" the player. The creator of the SoundSource can't Dispose it until the player's done, but will have no use for it afterward, so the most convenient course of action is for the SoundPlayer to dispose of it.
I would suggest that if both scenarios are at least plausible, you should either provide a factory method which transfers ownership of the IDisposable along with one that doesn't, or else you should have a factory method with a parameter that indicates whether ownership should be transferred. Note that passing IDisposables to constructors for classes that are supposed to consume and Dispose them is dangerous because Microsoft does not allow try/catch blocks around constructors invoked from field initializers and it's difficult to ensure things get disposed when a constructor throws. Having a factory method call the constructor makes error trapping much easier (though it's still a pain--especially in C#).
Edit--Addendum
Another situation approach which is sometimes useful is to have an object either publish a Disposed event or accept a delegate in its constructor to be run when the passed-in object is no longer needed. I prefer the explicit delegate to the event, since using an event would imply that the event subscriber (the person creating the object that will temporarily hold the disposable resource) has an obligation to unsubscribe, which adds additional complication, especially if the object might be handed off to yet another object. Since by far the most common thing the caller will want to have done when the recipient of the object no longer needs it is for the object to simply be deleted, the simplest case is to simply have an option for the object recipient to handle disposal itself.