It's not hard to understand why you would want free access to the lyrics and chords for awesome praise and worship songs. I would like to offer an explanation from the other side of the issue. Please understand that I am not trying to be hard on your or discourage you. Don't stop playing the songs, just try to understand the other side of the issue. This is a matter of law, not opinion.
While I don't write lyrics, I am a writer and have a little understanding of copyright law. I say "a little understanding" because American copyright law is complicated and internet issues are making it more so. I am not a lawyer, but I am on the management team in several creative online creative writing groups and have had to research to answer my member's questions.
Integrity Music more than likely does not own the copyright to the lyrics. I know the liner notes probably do say so on the CD and sheet music, but that is a standard practice within the industry. Just like when you buy a magazine or a book, the copyright might say something like "Copyright 2000 Macmillan USA", but that is the copyright for only that specific edition of the book or specific issue of the magazine. The copyright for the book, article, lyric or music remains with the creator.
"Copyright" is a broad term that covers many facets of the actual usage of the intellectual property. Since I do not write lyrics, let me break it down in terms the sale of a short story. Say I submit my story to a magazine that prints fiction. They like it. They send me a contract offering to buy the First North American Serial Rights to my story. I like the offer. I sign the contract. Depending on the terms of the contract, I might be able the next week to offer that same story for publication to an anthology publisher. I did not sell the magazine the anthology rights, so I can do this. Perhaps the magazine prints an anthology once a year of the best of their fiction offerings. If they wish to include my story they must either specify that in the original contract or send me another contract. I am still free to sell the movie rights to this story, use the characters in another story, expand the story into a novel or whatever else I wish to do with it since I still retain the basic copyright.
Legally, the publisher is bound to protect the works they publish against copyright infringement. Integrity Music more than likely had no choice but to press that web site to remove the lyrics since there was no negotiation with the artist to allow their lyrics to be published on the web. It was most likely at the request of one or more writers who did not like their works published on the net.
It is one thing to learn the song yourself by trial and error and to share it in praise and worship and another thing altogether to be angry because the publishers and artists/writers stood up for their legal rights. Work the chords out yourself, it will make you a better musician. If you can't work them out alone get help, if that fails, buy the sheet music. I know that it can't be cheap, but to expect the creator of the songs you love enough to want to play shows a disregard for the time and God given talent of the writers. Yes, it is your God given right--actually it is a must not a right-- to offer God praise and worship, but it is NOT a God given right to have free use of whatever song you choose regardless of the wishes of the creator of that song. To spell out the worst case scenerio, the creator of those songs could bring legal action for just playing their song, but none would be willing to ruin their careers with such an uncharitable action. It would, however, be totally within their legal rights.
One last comment about intellectual property. As soon as anything creative is set in permanent form it is technically copyrighted. The legal process one goes through is to REGISTER that copyright. Those guitar chords are legally copyrighted as soon as they are written down. They are an original composition that once read or played would recognized as a certain song and are protected by copyright law the second they are written down.
(I didn't mean to write a novel... sorry)