Surviving Termination

All provisions of this Agreement which, by their nature, should survive termination, shall survive termination, including, without limitation, ownership provisions, warranty disclaimers, and limitations of liability.

The above is an actual provision in the T&Cs (terms and conditions) of a Silicon Valley venture-backed company. Our experience with their customer support, their technology, and their communication is that they are all screwed up.  Noticing the details of their contract further confirms this view. As in, who is to decide if the nature of a provision is that it should survive termination. For example, does the  indemnity that they required of us survive termination? Of course, it doesn't, I think.