The publisher chooses the order in the waterfall for header bidding. Due to its nature Header Bidding is serial in the page and only a limited number of partners can bid on the page (4-5) and are called sequentially. Header bidding was created to increase competition for premium inventory beyond Google, so naturally Google ends up being used as remnant inventory in these cases because it’s always able to fill inventory, but not necessarily at the highest price and it’s thus placed last often but it really depends.

Also recently Google has shifted the auctions to unified pricing which means 1st price basically and a single floor for them to make their prices more competitive in header bidding, so this might have had effects on Google’s position in the waterfall as well given what the publisher want to accomplish.

Generally speaking the article is overall fine, there are some historical inaccuracies of sorts and innovations aren’t explained well, for example Google didn’t just start to track people because they figured, but because behavioral targeting retained customers of all sized as opposed to just the bigger ones that do brand awareness campaigns, and that was due to measurable superior performance.