So what you are saying is that you want the browser form to NOT tab to the icon, right?
Either way, it is difficult to compare browser form behavior to native form behavior as they are two different beasts. Its possible it was an oversight when the browser form engine was developed, or it could have been intentional. I would not plan on having behavioral changes to the date picker.
My guess is that it was intentional. In the native form you can use Alt+DownArrow to open the date picker using they keyboard and that this is not an option on browser forms, and so for accessibility reasons, they included the icon in the tab lineup.