Edits are there to improve the presentation of the author's content, not to change it. Their goal is to make the reader better comprehend whatever it was that the author was trying to say.
If you would like to add entirely new content then the appropriate medium to do so is either through a comment to the answer, or if you are providing enough content that you feel it is worthwhile, an entirely new answer to the question. (Just be sure that if posting a new answer, it fully answers the question, and that it's not just a reply to another answer.)
The rejection of the edit was correct, and for the correct reason.
That the answer is accepted has no bearing on this decision.
If a post is marked as Community Wiki, though, that changes matters entirely. The whole point of marking a post as CW is to say, "This post is no longer just mine. Anyone and everyone is free to change the content of the post, not just its presentation." If the post is marked as CW and there is a suggested edit that changes its content, then approve/reject the suggestion based on whether it is correct, and whether it improves the quality of the post. It is under no obligation to maintain the authors intent.