This is actually intended and accurate behaviour, it just isn’t desired for your specific use case.
To put it another way, when you click on bar, by your logic home should not be active, but it will be, because home and bar are the same page, with the same URL. Thus what you want is ambiguous.
Instead I recommend you download and install the Spots plugin. Create a new Spot with the content from the bar page, then insert that spot into the bar page. Finally, create a page called Home, and set that as the frontpage, and hey presto, home != bar and the menu works as desired, but they both show the desired content.