Hi Doc,
I am not sure about the US, but in Italy (I believe it is similar in the rest of Europe) a cover band, (or an original group) will hand a list of their set (with the authors listed) to the club owners. The club hands over the set lists nightly and pays a royalty fee (this varies from club to club) based on several factors to the local copyright collection society (SIAE in Italy, it would be Ascap or BMI here in US). The society then allocates the royalty collected from that club to the songs from its playlist database for that club.
Now about the Tab law. This is not really about stopping you, the customer, from having access to Tab, or sheet music. This is more about the companies having to enforce protection of their copyright; if you do not do protect your copyright you can legally lose it; an unscrupolous person can take advantage of that and it's been done more than once; they could start making copies of your work for sale and argue that since you did not defend it previously it means it's not that important to you and should go into public domain, thereby making their sale of your work legit.
Also, music companies don't like seeing sites who, sure, may be giving tabs away for free to you, but often are making money themselves because of advertising and other things that bring in money (like selling data that they accumulate through traffic generated on the site). That's not fair, they are making money on the back of other people's work without their consent. And even if you are totally losing money while giving away tabs, it's still not legal, and the copyright protection issue still arises.
What I'd like to see is the Music companies themselves offer this service, either by legally licensing it or by having it on their sites. I'd like it to be free, because I think it's great advertising but I'd be willing to pay a fee of a few bucks a year for the service even though I'm trying to read more music and less tabs.
Valentino