"Near Death Experience" is relatively new a term for those suffering close to an absolute death of the body if not indeed an actual death.
Saints in the past may have been recognized to have physically died because others didn't know if death had actually come. You're right, though, that the Church is very leary of all private revelations. It takes a good deal of prayerful discernment to understand and a lot of joyful patients for God's answer.
Certain Saints are known to have divine visions gifted to them because such men and women have dedicated their entire lives to a devotion to Jesus:
of St Thomas Aquinas, would his ectasies have been concidered "near death experiences"?
"Towards the end of his life he had a divine revelation in the Chapel of St Nicholas in Naples it caused him to state,
"I can no longer write, for God has given me such glorious knowledge that all contained in my works are as straw - barely fit to absorb the holy wonders that fall in a stable," Three months later he died."
http://www.poetseers.org/spiritual_and_devotional_poets/christian/st_thomas/
I tried to search for St Don Bosco's life concerning a near fatal illness he suffered. Apparently close to death, he struck a deal with the Virgin Mary who interceded to extend his life that he may continue helping the children he adopted from the streets. This may be another example of a "near death experience".
Some of these visions of life after death may be true. Certainly the ones recorded in the New Testament (e.g. Book of Revelation) are true. But the "default position" on such [rivate revelations and visions should be scepticism because of the overwhelming propensity of us human beings to get muddled up in pur minds.