A “claim” made by an mere officer does not commit the U.S. to ownership of anything. Such ownership decisions are made way above their pay grade. Ownership claims have never been by the U.S. government. The Russians have made ownership claims, and enforced them on the islands themselves.
Your quote was “2) The U.S. has never actually claimed the islands. Russia claimed the islands back under the Tzars.”
My point was that the officers of the Jeannette Expedition did in fact claim the islands as territory of the United States in 1881. After drifting in ice floes in search of a Northwest Passageway for 2 years, they discovered the islands, Russia did not. This is published fact in many historical documents and disputes your statement that there was no such claim.
A direct quote from the log journal of George Wallace Melville states, “...I, as a commissioned officer and proper representative of the Government, landed first; and, having claimed the island as the territory of the United States, invited my companions on shore...” (pg. 21 of “In the Lena Delta”, in reference to the discovery and naming of Henrietta Island.)
Your original statement was erroneous and deserved a fact check in honor of the men who died in service to this country.