The brain doesn't die immediately when the heart stops pumping, otherwise people could never get revived. People could be simply dreaming.
I have been personally acquainted with two people who both claimed to have died, visited the other side and returned. One was woman who, as a girl, nearly died. She said she could see the surgeon operating on her and that he said "I've never lost a child before and I'm not going to start today!" She then said she met Jesus and was told she would be ok. She fully recovered. I said to her "It must have really strengthened your faith". She responded "It's not faith, it's FACT!".
I knew another woman, a low-key accountant that kept mostly to herself. In the course of conversation I learned that she nearly died during childbirth. I asked her if she had an NDE. She said she did. She said she knew she was "dead" but had total peace and was ok with it until she thought that her baby would grow up without a mother and then she was revived.
There are countless others, certainly way too many to discount as a lie, dream, etc.