re: What Do Tashlich and Kapparos Have in Common?

In the class recently re-posted here by Rabbi Bar Chaim (you downloaded it, surely?) the Rabbi states the Vilna Gaon would recite the verses of ‘Tashlich’ at home, but not go to bodies of water.

I humbly differ. The Gaon’s practice is known to us through the book Ma’aseh Rav #209 which states:

לא היה הולך לנהר או לבאר לומר תשליך.

But the meaning is he did nothing at nowhere.

This is because the words נהר או באר are a paraphrase of Kisvei Arizal, who Mishna Berurah (583:8) quotes saying this:

ובכתבים כתב נהר או באר וטוב שיהיה מחוץ לעיר.

Am I missing something?