Not sure how I can make this any more clear. The elderly (or anyone else) who need and qualify for Medicare can establish their eligibility/identity by using information that is not valid for the purpose of voting based on the laws that have been passed. It's really that simple. One can qualify for Medicare while still not having valid ID to vote.
Really anything government related that requires identification offers more options to prove who you are than voter ID laws. WHich is one of the big issues many opponents of voter ID laws as passed have had. They are too narrow and limiting on what is deemed valid.
Please do tell what documents a senior citizen can use to prove eligibility for Medicare that would not work to substantiate their ID for voting???
As a reminder, here is the list from your link:
Acceptable documentation of identity includes:
Driver's license or state identity card
Certificate of Indian Blood, or other U.S. American Indian/Alaska Native tribal document
School identification card with a photograph of the individual
U.S. military card or draft record
Identification card issued by the federal, state, or local government with the same information included on driver's licenses
Military dependent's identification card
U.S. Coast Guard Merchant Mariner card