I would imagine he means trying to navigate the debris when sending other stuff into orbit, or bringing spacecraft home. I've often wondered this myself... at some point do we have so much stuff up there it's near-impossible to get spacecraft out without serious danger to their crews? And what about when it's time to retire them?
If my napkin-calculations are correct, 4025 stats @ 1100 km LEO orbit would occupy 0.0000000573% of the sky - so not a real problem, I believe ;) (if they are in the same plane, that is and each have 10mx10mx10m bounding area...)
I'm guessing they are referring to real-estate capacity. Not including space junk there are about 2,300 satellites in orbit. This is quite a proportional increase and the risk of collision with junk will go up.
The collision risk will depend very much on the altitude at which they are placed... this is also a big determiner of design life (N years before the orbit decays and they come back into the atmosphere) and might also have some effect on signal strength / geometry.
Remember that this space is significantly larger than the total surface area of the Earth, since it represents a sphere larger than the Earth. Imagine the satellites are the size of an outdoor garbage receptacle. Do you think 600+ of them floating around really presents some risk of collision? There's probably more garbage bins just in New York City, and this is spread over an area much larger than the surface of the Earth.
Space is really, really large. Using the intuition you developed while living on the surface of the Earth provides you little help when thinking about space.
The asteroid belt, which is positively TEEMING with possible collisions... billions of objects... yeah, we don't even bother. Ninety-nine (point nine nine nine...) times out of a hundred you won't hit anything. Space is big.
Well, to be honest, orbits are more like corridors so the risk of collision increases a bit. But still, if they're at least a little bit careful about avoiding generation of space junk, there shouldn't be a problem.
For example, there are literally thousands of airplanes flying in the US airspace at any time. Now look up and see if you can spot one.
There's a lot of empty space up there. Even more so 200 miles up.