Hi, Bibiomomiac,
(I hope that you are a lover of the Bible, as am I.)
It’s a good question you’ve asked. (First, simply, Latter-day Saints don’t think or “assume their church to be the only ‘real’ Christian church”. “Authorized church with continuing revelation to guide its leaders in leading people to the ordinances and covenants centered in Jesus Christ that lead to exaltation through His grace and His shepherding influence” would be a way you could put it that would express the thinking.)
If you would like to understand the Latter-day Saints perspective about how it could be possible that God would inspire the writing of beautiful, wonderful hymns of praise by those who were no doubt experiencing His love and blessing in their lives, then perhaps it would help to think of a “truth source” with pure truth beaming across the universe and available to all. (God is no respecter of persons, right?)
As humble, prayerful people have sought truth and guidance in their lives from that “truth source”, then they have certainly been able to receive truths and guidance and blessings which are always promised through obeying those truths. That would include the inspiration to write beautiful hymns of praise and adoration. Those were “real Christians”, with real love for Christ and the real inspiration of Christ and the Holy Spirit.
I haven’t heard the term “dead churches” used in my church, nor do I believe that terminology for a second. An individual person can be “dead to Christ” by having experienced “spiritual death” through having rejected their conscience and rejected the influence of the Holy Spirit in their personal life, but that doesn’t mean they have belonged to a church that led them to that point. It means they weren’t paying attention, if their church used the truths from the Bible as the basis for teaching about living the gospel of Jesus Christ.
They can be spiritually alive and spiritually awakened as they read the Bible and live by its teachings, including seeking inspiration from God through humble prayer and their desires to have the love of God in their heart and to act on that love in how they serve the people around them.
Sorry for the long answer to a short question.

Wishing you peace and a wonderful day.