Yes it's a violation of the law, but much like any other laws, there are defenses to these built into the laws. For example, for murder, if you kill someone, you commit murder (or homicide or whatever word is used), but there is a built in defense that you are allowed to do this in cases of self-defense. So still guilty of the crime itself, but the exceptions make it not a criminally punishable act.

Similarly, in copyright there is the concept of fair use. Again, any copy you make of a copyrighted work violates the copyright act, however there are scenarios where the copying becomes not a punishable offense. In copyright, these are usually things that there is a benefit to society that outweighs the detriment to the copyright owner such as transformative art which creates new art, or backup for purposes of archiving. So likely the copy itself is protected here. The potential issue comes in the fact that they then share that copy. This is where the legality becomes murky as copyright law in the US has never been updated fully to deal with digital copies which take miniscule cost to produce and are nondestructive of the original.

But let's assume that the law supports the music industry. Then we move to harm. How much harm has been done to the owner. Since this is a corporation we're only talking profit, not emotional or other types of harm that might be involved. In this case they are claiming that for each work shared over the internet, they have been denied $150,000 in potential profit from selling those works.

This is where the real issue comes in in that courts rarely dispute these ridiculous numbers. IMHO the fact that they are pitting these kinds of numbers in a court document sounds like fraud to me. For much of this work they have no actual copies of the works because they were destroyed or deteriorated. So how could they sell them and make profit? For what they do have, is there even much of a market for any of that content and would that market generate $150,000 for a single random song written many decades before most of us were born. Sure the award will likely be less than that, but I bet the average song on this list might generate less than $1 in the time from when they posted them to when their copyright finally expires. So charge them a few hundred dollars and be done with it.

The issue is that the works are otherwise not available for sale and any licensing is done across all works owned by these companies and this is how they get the $150,000 per work number. They don't sell licenses just for old works because the system was never designed to support copyright lasting as long as it does now.