It does in the civil context, but not in the criminal context, which seems precisely right.

In the criminal context, the government is trying to punish you with jail. Actual deprivation of liberty. In such cases, we require they make be able to make their case without you saying you did it.

In the civil context, you can avoid saying you did it if it would cause you to possibly be convicted of a crime, but unlike the above, there is no possibility of deprivation of liberty. As such, if you do try to avoid saying you did it, people are allowed to use it to make their case that you did it.