Does a BSD-licensed project need a signed statement from each contributor?

Question

Today I read on Fossil SCM's mailing list:

The problem with BSD is that you really should get a signed form from each contributor stating that their contribution is BSD. This is automatic with GPL, since releasing your contributions under a compatible license is a prerequisite for viewing the code in GPL. This makes GPL great for a highly collaborative environment, with lots of contributors. BSD is more permissive (less burdensome) for readers, but that makes it a little tougher for writers since they now have to send in some paperwork.

Could someone explain why, and what are the possible consequences of not having such a signed statement from project's contributors?