AS you surmise the Original device should be the one that is correct.
I have two iPhones and was using them both yesterday keeping my wife informed of my progress home from London to Bournemouth railway station.
She apparently sent me replies which I did not see until I returned home and was reconnected to my WiFi network.
Right this second at home I have iMessage the wife and have heard her phone in the lounge (she has just gone upstairs).
My Mac version says "Delivered" but has not changed to "Read"
My iPhone's synced version agrees with the Mac version once I open Messages on the iPhone.
So my own experience is that iMessages to phone that can only get SMS messages at the time do not always get delivered and the indicator on the iPhone and/or Mac version is right in waiting to show it.
This leads it to being about what sort of service the other actually has at that moment.
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously