I believe there are 2 main reasons why a user would send you a private message instead of a publicly available one (in the context of reddit or similar sites).
1) They fear other users might jump the bandwagon on the negative part of their message and want to spare you the humiliation that might come with it.
2) They don't want to become the target of people not agreeing with their point but think it's important enough to let you know.
In the first case you don't really do anything wrong with quoting them directly (preferably with name to give them credit).
In the second case you should never leave any identification on who wrote the message. If you do they might still fall pray and can't do anything about it. This will feel like a big violation of trust.
The problem is that you can never know for sure which of the 2 cases is relevant here as long as they don't confirm that you can quote them.
In that regard I agree with Monica Cellio's answer that you should be careful with publicly posting anything that was sent to you in private.
What I would do is decide whether the message itself is really important or only the general point it's trying to get across.
If the message itself is important, for example if you don't know if you interpret it correctly, then it makes sense to directly quote it. But I would anonimize it except if you have permission from that user (or know them well enough personally to know they wouldn't mind).
If only the main point is important you are probably better of not quoting the message at all:
I have received a message/messages that my work lacks the rigor of a standard math paper. [continue with point you're trying to make here]
If they really wanted credit for complimenting/insulting/informing/... you they would've done so with a public reply instead of a direct message.