Claiming a non-resident relative who lives in Mexico as a dependent

I want to claim my mother-in-law as a dependent.  She is a Mexican citizen, but has never been to the U.S. and does not have an ITIN number. 

 

According to Rules for Claiming a Dependent on Your Tax Return - TurboTax Tax Tips & Videos (intuit.com) page, under the "What qualifies someone as a dependent?" section, "The person must be a U.S. citizen, a U.S. national, U.S. resident, or a resident of Canada or Mexico. "    She also falls below the income threshold and I provide more than 1/2 of her financial support.  So it seems I should be able to claim her as a dependent.  

 

However, when I applied for an ITIN number for her, I got a letter back saying that she needed to provide one of several original documents "... showing her name and U.S. address."  

 

So I am confused.  Does she require an ITIN number before I can claim her as a dependent?  And if so, how can I get an ITIN number for her if she does not live in the U.S.?