Yes you are right from a Retail Trader perspective. (If you have Stocks and you want to protect your stocks you have to Buy Puts and not Sell Puts because there is no Shorts possible in Stocks.) But from a Market Maker perspective, They Can Go Long and/or Sell Short. So they create a Range for the Retailers to play. So let us play within that Range. Sorry If my explanations are confusing. What I wanted to say was Market Makers try to create a Range for the Index or Stock, which is visible using the MAX (OI).
If you don't believe me watch the movie - "Rogue trader". Its a true story about a guy who was a market maker with extremely deep pockets. He did go bust simply because he didn't accept he was wrong.
Hedging a long position never involves selling puts. That's completely ridiculous whether it is from a retail perspective or a market makers perspective.