I think your question is a little too vague.

In general case DCnets provide perfect sender privacy (among participants, of course). If there are multiple messages their senders will be completely unlinkable.

Specific implementations might use schemes for collision resolution that break privacy, though there is no requirement that collisions (absent malicious participants) even be possible at all-- with fancy enough technology applied.

Dining cryptographers and their variants are usually fully proven in the sense that when all but one input is zero, you will receive the intended input. You always receive the combination under the operation you are using (i.e. xor of all messages).