The distinction that conversations are protected by BOR limitations on search until they are in the possession of the foreign agent has been and still is effective for letters, but isn't of any use in the case of instantaneous electronic communications. Apparently the standard that such communications that originate in the US have BOR protections is what is evolving to replace the old standard. Personally, I'd keep Madison's precedent- though I see that it has it's faults now too.
American presidents have always had inherent constitutional war power to "repel sudden attacks" (and sole power to deal with foreign agents).
Of course it is a very dangerous power which could destroy all our freedoms. Nixon resigned before certain impeachment for apparently abusing it.
Any president who didn't use it to defend the country from a foreign attack would also face certain impeachment.
...Though the media would be able to lie enough to save a Dem president from a 2/3 Removal vote by the Senate.
Correction: I don't KNOW that ALL the papers were "acquired inside this country". The spy, John Henry, came to DC but some of the papers presumably were already in our possession as bona fides of what he was selling- for $50,000 BTW.