Excel Solver Constraint returning TRUE or FALSE

You didn't say where you are seeing the TRUE and FALSE values.  But, If the problem is SAVEd then that's what you will see.  So, I'll assume that's it.  
One thing that may be helpful to know is that the Solver problems belong to a specific worksheet.  
When the problem is SAVEd, the process appears to assume that the worksheet remains unchanged and it saves formulas for the constraints without a worksheet name: e.g. for the problem in worksheet "Model":
it will save $O$5 <= 7 instead of Model!$O$5 <=7
So, if this is saved in Problems!A1, this formula will say O$5 <= 7 so pointing at Problems!$O$5 which may be blank and, thus, FALSE.
I've never seen a solved problem generating anything but TRUE on the same worksheet.  But, there may be examples where this could happen.  I'd be very surprised if it results from a solved problem though!!