Not so. Paul wrote the book of Philippians, especially chapter 4:4 which this hymn is based on, while in prison in Rome. He himself had been beaten, stoned and had his life threatened numerous times.
But this rejoicing isn't a call to throw a party. This is a rejoicing in the Lord. A deep, abiding, hopeful trust in his care for us. Philippians 4:4-7 says this:
4 Rejoice in the Lord always; again I will say, rejoice. 5 Let your reasonableness be known to everyone. The Lord is at hand; 6 do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God. 7 And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus.
Our rejoicing comes from a life of prayer and trust. We come to the Lord with thanksgiving for all he has done for us and with our petitions. We lay aside all anxiety and, in doing so, Christ fills us with peace. For this, we rejoice. We have a sovereign God who is in control of every aspect of our life - good or bad.
There is no better reason to rejoice than that.
Rejoice, the Lord is King! Your Lord and King adore; mortals, give thanks and sing, and triumph evermore. Lift up your heart, lift up your voice; rejoice; again I say, rejoice. 2. Jesus the Savior reigns, the God of truth and love; when he had purged our stains, he took his seat above. Lift up your heart, lift up your voice; rejoice, again I say, rejoice. 3. His kingdom cannot fail; he rules o'er earth and heaven; the keys of earth and hell are to our Jesus given. Lift up your heart, lift up your voice; rejoice, again I say, rejoice. 4. Rejoice in glorious hope! Jesus the Judge shall come, and take his servants up to their eternal home. We soon shall hear th'archangel's voice; the trump of God shall sound, rejoice!