This isn't really an enhancement request, but I've been told this is the correct functionality, despite the fact that it confuses every single one of my users, and that the only way to get it fixed is to request an enhancement. 

When we do a Basic search, for example, all approved grants, except those that have the status closed or withdrawn, we do the following (this is from my help conversation with support staff):

Disposition = Approved - then Request Type and status ->  is not = Grant/ Closed Grant (112) + is not = Grant/Cancelled -Incomplete (5163) + is not = Grant/Cancelled - Withdrawn (5164) 

If we just run that basic search, we get incorrect results, that include projects that are Closed or Withdrawn or Incomplete.  According to support, in order for this basic search to work, we must then go into the SQL search string under Advanced (which is terrifying for my of my basic users) and change all of the 'or's' to 'and's'. From the support email:

NOW, change the OR's to AND's 

Requests.Disposition = 'Approved' AND (Requests.Status_ID <> 112 OR Requests.Status_ID <> 5163 OR Requests.Status_ID <> 5164)

to 

Requests.Disposition = 'Approved' AND (Requests.Status_ID <> 112  AND  Requests.Status_ID <> 5163  AND  Requests.Status_ID <> 5164)

This seems like a flaw.  If the Basic Search is supposed to take the thought out of creating a SQL search string, it should translate to the correct search string.  My basic users are never going to be able to modify SQL search strings, which means I'm going to have build searches for them whenever they have something which should not be this complex.

PLEASE FIX THIS SO THE BASIC SEARCH DOES WHAT IT IMPLIES IT DOES. By having it not actually return the correct search, we risk users running incorrect searches, not noticing, and providing invalid data.