Consequences of inrush current out of specifications in AC/DC power supply
The inrush current of the GST160A15 applies to its inputs i.e. how big the surge of current it might take when it is initially powered. This isn't an output spec for anything connected to it's outputs; it's an input specification.

The inrush into the control card may well be what you said but that does not relate to what the Meanwell power supply takes from its power source.


  Could the failures be entirely due to the inrush current over specs?


No but you need to read the data sheet carefully about what current may damage the Meanwell supply due to an excessive load on the output however, I suspect that it protects itself.


  Or are they other possible reasons?


Yes, possibly other reasons that may not be at all related to the observations posted in your question.