Yes it's true XYZ Music Corp would only own that performance (as it's Beethoven and the piece is long out of copyright). The problem is, the automatic filter is a fuzzy matcher: it compares the upload against every other performance of Beethoven's 5th it's been programmed to recognise.
Let's say our uploader has been learning from one of those performances. Their performance will sound very similar to another pianist's -- at least to the fuzzy-matcher.
And therein lies the problem: the uploader's piece is clearly copyright to them, but the magic upload filter can't tell the difference.
It's like uploading a silent theatre production (let's say some kind of homage to silent films) and the upload being flagged for violating the copyright in 4'33".