Why, when most people sing (in English), do they ...

Hello Andrew, when people sing they repeat sentences they have already heard of, furthermore when people sing it is harder to notice their accent.

But when a person wants to build a sentence by himself, he will say it with his accent

I added an article about accents from the "Linguistic Society of America" institution.

http://www.lsadc.org/info/ling-faqs-accent.cfm

It's like Mel Tillis the country singer that stutters...rhythm.  Also as zo-808 said repeatition.  Most people when they sing (no matter in what language) will sing the song the way they learned it (in many cases how it is song by a professional artist) thus they are just repeating what they heard which is exactly how people learn to speak to begin with.