streaming is downloading, otherwise it wouldnt be visible on your hardware. if you pay for a stream and the distributor downloads it to your buffer, the only thing preventing it from persisting is wrapping the data to contain it in a file structure. if we really want to split hairs, everytime the data is accessed a streams bits are copied into registers, but those bits have no identity beyond 1 or 0
if you dont distribute this to others or brag on a forum about all your streams, no one will even know.
There is a good epigram about DRM that goes something like
"Asking a computer to not copy things is like asking water to not be wet."
The argument is that it doesn't create another copy, so it's more analogous to receiving a broadcast. Like, if a pirate radio station plays copyrighted music, then the mere act of receiving those signals isn't a copyright violation. But recording that broadcast would be.