Does the Rhine pass through Italy?

No, it passes only through: Germany, Austria, Liechtenstein, Switzerland, France, Netherlands

https://en.wikipedia.org/wiki/Rhine

It says in the same article that the Rhine Basin is situated in Germany, Austria, Liechtenstein, Switzerland, France, Netherlands, Luxembourg, Belgium and Italy. Can anyone explain why Italy is on this list?

The Italian section of the Rhine is called the Reno di Lei.

https://en.wikipedia.org/wiki/Reno_(river)

The Reno River in Italy empties into the Adriatic and is hardly a arm, branch, or tributary of the Rhine. It is a separate entity. The Reno and Rhine do, however, share the same etymology.

https://en.wikipedia.org/wiki/Reno_River

The basin of the Hinterrhein (one of the two intial tributaries of the Rhine) includes the Reno di Lei, which originates in Italian territory. From what I can tell it flows from the Lago di Lei, a resevoir in the Valle di Lei, in Italy. "The waters of the lake are among only a few of the waters in Italian territory which end up in the North Sea, being part of the Rhine's drainage basin."

https://en.wikipedia.org/wiki/Lago_di_Lei

https://en.wikipedia.org/wiki/Hinterrhein_%28river%29