The nature effect is not a substantial reason to say Hinata is dead.
Remember Choji and Neji nearly died and Kishi used peaceful nature as a backdrop for a death teaser.
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So using nature is not always a clear case of death. Look at Pa frog. No dramatic effect of nature. Nor Ma frog (if she is indeed dead too.)
And even though I believe Pain can see chakra and Naruto can sense it. I am hoping her chakra is just low and that Pain knows it only to make Naruto get emotional and trigger the nine tails.