OK here is what INM told my partner when he contacted them yesterday:
I just called to INM to the 800 number. I was told that that yes, in fact ( I would say in theory) the form FMM should be delivered at the INM at the MEX/USA border when Canadians and American Tourists leave the country, the functionary told me that it is true, that some times there are no officers to claim or pick up the document so you can keep it handy just in case as a future reference, when you access again to Mexico, there are no penalties on this so it shouldn't be a reason of worry for our visitors...
