That sounds like a piece of folklore not based on real experience. Trout have to deal with things floating over their heads day in and day out. Think of conditions in the fall with all those leaves floating by, or windy days when all manner of junk is being blown across the surface. Those conditions can produce some of the best fishing of the year.
Anything that seems unnatural or out of place is likely to spook a trout- or any other fish for that matter. A streamer appearing in front of their vision very suddenly (unnaturally) is just as likely to spook them as a shadow cast by a flyline floating overhead.
On heavilly fished bodies of water fish can become very "educated". Anything less than a perfect presentation is probably going to be treated with disdain whether floating or sub-surface.
When sight fishing, look over your shoulder from time to time, you never know who's behind you