Ok,so I read and reread all the previous post regarding this matter and this is my take on your situation.
The company only wants to know if you are entitled to park in the handicapped designated area. As per Texas law,YOU may park in any handicapped designated area for any unlimited amount of time as long as YOU are the person with the disability and YOU have the appropriate placard or plate. Also, YOU, may park in any designated area, as long as a PERSON with a handicap is with you.No brainer.
If YOU are a fully functional person with no disabilities, but have a handicap or placard plate on your vehicle,to transport a disabled person by need to stores or appointments for their benefit, then YOU can`t and shouldn`t be parking in handicap spots when that person is not with you.
Just because you have a PLACARD or PLATE for handicap parking YOU need to use discretion how you use it.
If it`s for YOU and you need it, use it!
If it`s for convenience, think twice.
MY TAKE ON THIS: If you have a legit placard or plate that allows you to use the designated parking area, for YOU, that was issued to YOU by the State of Texas, then all you need to do is provide your parking privilege placard and nothing more. NO MEDICAL RECORDS WHAT SO EVER!