And there is a difference between תחתיו and במקומו (in its place): במקומו includes a large boundary that is unique to a certain thing, but תחתיו is only the place that is under it.

And the word תחתיו may refer to a thing that is on the side of something, while being lower than it.

Genesis 29:26 says, ויאמר לבן לא יעשה כן במקומנו לתת הצעירה לפני הבכירה (And Laban said: 'It is not so done in our place, to give the younger before the first-born’), using the language במקומנו for “our place”. This means the whole city⁷⁰⁸.

footnotes: ⁷⁰⁸ Malbim, HaTorah v’HaMitzvah Tazria 108.