Does the sentence
"The quote reflects a Catholic view of heaven."
mean the same, as the sentence
"The view expressed in the quote is what Catholic Church teaches about heaven"?
In this context, "reflects" most nearly means "shows". For example, the sentence you gave:
The quote reflects a Catholic view of heaven.
means the same as:
The quote shows a Catholic view of heaven.
The two sentences mean almost the same thing, but not quite.
If you say, "this reflects the Catholic view", you mean that it is consistent with the Catholic view, but not necessarily the official position.
For example, someone might say, "This book, where people live side by side with angels in eternity, reflects the Catholic view of Heaven" might well be accurate, because this is consistent with the kind of things that Catholics say about Heaven, even if there is no official Church doctrine saying that people and angels live side by side in Heaven. (This isn't really the best example, but I can't think of a better one off the top of my head.)