I did a little more research - this has been bugging me. I'm thinking this access might be OK see details below. But I'm still bothered that only jonoro and myself have reported this problem.
I found two copies of WMI on my system. One in C:\WINDOWS\system32\wbem, the other in C:\WINDOWS\system32\dllcache
They appear to be identical - same size and version. Both were modified Feb 6, 09.
I've read that ...\wbem is where it belongs - and that copy has a create date of Aug 16, 05 (which makes sense).
The one in ...\dllcache is a little more worrisome - it's create date is April 15, 09 - which is about when the problem started.
I looked in the event log (using the MS Event Viewer - part of the MS administrator tools) and looked for April 15th. There was a Windows Update at exactly the same time as the create date of the copy in ...\dllcache.
So this is *probably* legit version.
Anyway the next time it comes up - I'll check to see which copy is requesting, grant it access and see if it appears to make a difference.
Not unusual for duplicat/triplicate and even more copies to be found in windows directories and folders.