What about quantity invoiced?

You get a back order status even if the qty ordered = qty = qty invoiced received but the dollars received do not equal the dollars invoiced. 

Mismatched $ should post a variance, not leave the line / PO open for just $... unless I'm missing something?

As Kevin M mentioned, does the Quantity Invoiced match the Qty Ordered and Qty Received?  A Received PO will stay in the Backorder status until every line item has three point matching.  The Qty Ordered = Qty Received = Qty Invoiced must match to be marked as Complete.

Not true - just makes a variance.

I have this occasionally happen with one particular client.  We can see the receipt in Receipt History, but the Qtys on the LINEs still appear to not be received (but there is a total received amount on the Total tab).  I have to DFDM the qtys, then pull up the PO, save it, and it changes its status to complete when saved.  I've tried to figure out what they are doing differently, but all looks OK.

There are several reasons this can happen, the most common being the invoice was done in AP instead of PO.  See Article ID 222924450018964  How to complete or resolve backordered purchase order on the Sage 100 knowledgebase.