Whether or not it may have been a factor in the lack of advance notice to the public or to the sheriff about the exercise, the gray Mi-17 seen during the exercise is a dead ringer for Hips tied to a highly secretive U.S. Army element known as the Aviation Technology Office (ATO). Previously known as the Flight Concepts Division (FCD), ATO is headquartered at Felker Army Airfield, which is part of Fort Eustis in Virginia.
In addition to gray-painted examples, ATO-linked Mi-17s have also been seen painted tan and wearing a tan-and-brown camouflage scheme. These helicopters have a distinctive configuration that includes a nose-mounted weather radar, a sensor ball turret under the right side of the cockpit, supplemental armor panels around the front, a large particle separator in front of their engine intakes, and various antennas on the fuselage and tail boom.
The reason I think these might be connected to Ukraine is there has been a lot of recent imagery coming out about Ukraine's use of helicopters and extremely low flying tactics in the war in Ukraine. I am talking VERY low flying tactics that would normally be considered extremely unnecessarily dangerous by other pilots for a helicopter pilot but become a survival technique in the extremely hostile airspace occupied Ukraine. Meters or less off the ground I am talking.
One of the main helicopters Ukraine would have the most consistent and reliable access to (and that is found in a lot of these Ukranian videos accompanying Mi-28s and other helicopters) is the Mi-17 same, which on paper isn't an attack helicopter nor a particularly agile helicopter given its large medium duty size and capabilities.
This origins as a medium lift helicopter give the Mi-8 family some fundamental advantages despite its size though because the helicopter is meant to haul large amounts of weight, which means when the helicopter isn't loaded up with lots of cargo.... LOTS of torque which means the capacity to wrench the helicopter quickly out of dangerous situations.. possibly the most important capability for safety in the end for low flying manuevers if a pilot flies smoothly.
The Mi-8 family is the most numerous helicopter ever made and is popular across the world, but I suspect these flights are to give somebody information on how to fly Mi-8s in a way that is useful for modern high intensity combat.. which could unfortunately be somehow related to the Israel/US attack on Iran but I am unsure if Israel would have any need for this kind of training or data beyond what they already have.. so the next natural explanation is US defense organizations attempting to help Ukranian pilots get more data about pushing the Mi-18 to its limit.
The US military has I believe supplied a number of these to Ukraine though I don't know the details.
The details in your own post undermine your conclusion. Ukraine has operated the Mi-8 family for decades, and is probably already familiar with low-level flight tactics over their own territory, which is a dissimilar flight environment to the US Southwest.
In reality this is more than likely pilot training for Southwest Asian operations. US still conducts some operations in the Middle East incase you weren't aware.
Mi8s, or whatever the derivative name is, that were originally designed for Afghanistan were rerouted to Ukraine so it is definitely possible. Also I don't think Ukraine needs advice on how to fly them, they need high quality flight data for modernized Mi8 variants they can use to make sure the modifications they make function seamlessly.
To be specific maybe really high resolution flight data taken by a ring of bell unmarked helicopters flying in close formation to the Mi8? Maybe, maybe not.