Actually, if it was a design flaw, all refrigerators would automatically leak when the lines froze. This is not an Amana-specific incident, nor does it occur with this brand any more than the others.
The key here is to prevent freeze ups. This is done by regulating carefully the freezer temps and airflow. Too cold will get you frozen up quick. (Think 0o)
You can always glue the connections in place back there if you are paranoid about them coming apart in the future. There's no practical reason they need to be removed anyway. Any ice buildup can be quickly removed by heat gun or steam anyway.
In some cases where the freezer temps cannot be well maintained, we have installed tubing insulation inside of the freezer to protect the line. (Black foam tube sleeve)
One note of interest is that Amana does not recommend having the system connected to an R/O filter, nor a saddle valve. The incoming pressure must be at least 25 p.s.i at the water valve to keep it functioning properly. Too low and the valve may stick open.