I would expect it's the sheer number that would be BELOW the ISS. Active tracking or not, there's already plenty of things that influence when you can launch to the ISS. Having to navigate a route through 10,000 satellites between the earth and the ISS is just adding another obstacle they don't need.
The article seems to make clear, they can get this if they clear it with NASA. The implication being NASA believes this will be a problem for them, and if I had to choose who to believe between a company run by Musk, and NASA. I'd choose NASA personally.