Giving companies direct liability for policing copyright in user-uploaded content is a much bigger disaster, on two separate fronts, both highly damaging:
1) Implementing youtube-style content id will be a huge burden for small companies. Youtube reportedly spent tens of millions on it over several years. This tilts the field in favor of large incumbents even more than it already is by nature. While the amount of content to screen is really small, human-driven filtering is a possibility, but as soon as you need to scale up you're screwed. Any startup in Europe that needs to do this is a no-go from now on, IMO.
2) Back to that multi-milion content ID system: it sucks. It sucks really badly. It over-reports infringement left right and center. Now imagine what it will be like when youtube is liable a priori for every false negative; any sane legal department is going to demand a minimal number of false negatives at any cost. Now imagine what that will do to the false positive rate. Now imagine what the false positive rate will be when every site has to bodge together a similar system, with neither google's money nor google's technical expertise.
The second point has been missed by most criticism of the Copyright Directive, and to me it's the biggest problem of all. I fear the wasteland that will result. Are we going back to the point where only a handful of content producers exist and everybody else should be content just consuming it? Welcome to the 20th century, Europe.