OK, I can see why the buttons being outside the tab would make sense, but it doesn't make sense for the location bar to be outside the tab, as what it displays is unique for every tab.
There is no difference between those buttons and the location bar.
The location bar shows the URL field for the current tab. It also uses global state, for instance browsing on one tab adds completion entries to other tabs. Should it be outside the tab because completing is global and not specific to a particular tab? No, because what it displays and how it operates is irrelevant to where it should be located. What matters is what visual grouping the element belongs to, and this is not the tab because the presence of the element is not unique to a tab.
Take another example, an SVG editor. What buttons are active and what is displayed (font, color, etc) depends on which object is selected. Does each object get a separate Font text field floating within its bounding box just because the data varies per object? No, that would be madness. The location bar per tab is just a degenerate case of this, but the same principle applies that controls are shown at the outermost layer where the element is always present.
Lets also put it in another way. The purpose of a tab is to switch between different views. Suppose the bookmarks bar, buttons, and location take 20% of the window. With tabs at the top, switching tabs changes 80% of the tab's area, plus a little bit extra for the URL and possibly different button states. With tabs at the bottom, switching tabs changes 100% of the tab's area plus some extra areas.
In terms of visual appearance, tabs in Chrome "sort of" switch between different views, but not completely. How would you explain what changes when you select a different tab? "The web page part is completely different, the buttons change what they show, and the bookmarks bar and menu buttons are unchanged" vs "When you select a different tab its contents show a different web page". I think you can see which is conceptually simpler and makes the most sense of the two.