Burley Flex Connector, square tube vs round tube, does it really matter?
These trailer hitches are interchangeable and I have no issues.  I'm using the round connector in the square tube since it physically fits.  I have put some miles on it on it hauling kids bikes, pulling kids in sleds (recommended to keep the rope out of the tire and carry a spotter), and a 90 mile weekend camping trip.  I have had no issues with it.  

As a bonus here I took a round connector out of another trailer that really has some miles and years on and put it on a new trailer (Trek branded Chariot).  The tongue was squared tubed and too small for the connector but I was able to take a stone grinding wheel to the connector and re-size and shape to get it to fit.  No issues found in it at all.