In response to a question whether or not one can perform melakhah as usual on Yom Tov Sheni Shel Galuyoth, Rav Ami responds:

be-yishuv asur, ba-midbar mutar

"...in the city it is forbidden, but in a desolate and uninhabited place it is permitted."

His statement seems to be recorded as the halakhah and no one appears to argue with him.

Does he actually mean this and if so what is the significance of it for our understanding of the nature of Yom Tov Sheni Shel Galuyoth?

Please cite your sources. Thanks.