This is an "Access Denied" error, which means that an your account has no rights to access "Provisioning Engine" COM+ application that runs on your MPS engine servers.

I found that there are some MPS service accounts that do not have access to MPS COM+ component. For example, MPS Web Service runs under an account that is a member of a group MPFClientAccts, but this group is not a member of the local group "Distributed COM Users" on MPS engine. As a result, MPS Web Service application receives "No Provisioning Engines Available" error. The solution is to add these groups to the local Distributed COM Users group on each MPS engine:
      MPFAdmins
      MPFClientAccts
      MPFServiceAccts
      MPFTrustedUsers

I am not a big specialist on COM+ security, but i have a feeling that this might result in some unexpected security issues. Some accounts might receive elevated security rights, so i am hoping someone more knowledgable will respond to this post and elaborate more on this issue.