This was completely non-obvious to me so figured I would blog it. To create a rule more than one pixel thick of a solid color use this format:

<mx:HRule width="500"
    strokeWidth="4"
    strokeColor="#1278A7"
    shadowColor="#1278A7"
    opaqueBackground="#1278A7" />

opaqueBackground is the key attribute since by default (and counter intuitively) rules are actually borders around a transparent rectangle.