It doesn't do that though. stabilizer sells HBD on the market for hive. Then the hive is converted to HBD in the DAO.
It does both. HBDstabilizer uses the convert smart contract on HBD in order to receive Hive, buy HBD on the market when it is below $1.
The sources I used on inflation were 
@socky's old posts pre fork, where he tracked Steem supply daily, and for periods he didn't cover (most of 2020) I checked web archive copies of steemd.com and hiveblocks.com (there are much fewer dates, but you can still see how much supply has increased in a year).
More recently both 
@penguinpablo and 
@arcange have started tracking supply daily in their DB's and reports.
RE: The rate at which supply of HBD is expanding is much faster than the r ...