No, there's a difference between dual meaning as in "different meaning" and dual meaning as in deeper meaning.  In the latter, both can be right, one is just a shallower version of the deeper meaning.

I provided both.  These are both true and yet deep. 

so it's totally off the mark for you to say "Your colleagues here say there is only one acceptable Catholic meaning to anything Catholic!"  It's rather an odd statement to begin with!