Disable shipping option & allow local pickup only at one location

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Most of the items I offer are available for either shipping or local pickup, however there are some I do not want to ship.  I created two locations for this, one "Default" the other "Local" which has Local pickup option selected.  Both Default and Local can fulfill orders online.  Products that I will either ship or allow pick up are available at both Default and Local locations.  Products that I do not want to ship are only available in the Local location.

I created a shipping profile that only includes the Default location.  I do not have a shipping profile for the Local location.  The shipping profile for Default shows this message related to the Local location: "Shipping options will not appear at checkout on orders fulfilled from these locations. Add rates to activate these locations."  That is exactly what I want.  What I think should happen is products that are only available only in Local will be fulfilled from that location, and since Local is not included in a shipping profile the only option should be Local pickup,  That is not how it is working though.  All products have both a Shipping and Local pickup option at checkout - even the ones that are only available in Local.  Am I missing something here?

Thanks for any suggestions you can offer!