Adding more info: I had a good conversation with the staff at the Wilderness Permit office. This weekend is (was) the official fishing season opener. A bunch of clueless folks brought their RVs and travel trailers, without first checking on the situation. With everything (campgrounds, BLM areas) closed, people are parking their units every few hundred feet along Hogback Road, and other dirt road places. Whitney Portal Road's parking lot at the "road closed" sign is full of these.
Also, there is an undercurrent of anger in some of the locals toward people coming into the area despite the travel bans. Apparently there have been a few tires slashed (multiple, not just one, so how are they gonna leave? People can be crazy.)
As of now, the trail permit system has refunded reservation fees through May 15. Things are so bad, the "bunkhouse" housing for Inyo seasonal workers is closed, so they can't/haven't even hired the workers at this point. So when things open, there will still be some time to get everything up to speed.
The Inyo "developed" sites and Visitor Centers will remain closed until the county officials decide it is time to open things up. The county governments are controlling the situation.