Thank you both for your replies.
The screenshot below shows an example of the mail I receive when someone sends a private message. It says at the bottom of the page that I can reply to this email to respond. I get the same results when I get a mail about a topic.
When someone assigns me I receive a different mail. It only gives me a link to click on, and not the reply by e-mail option.
Just to be safe I have included the settings you asked for:
Manual polling is not enabled, but the pop3 polling happens every 1 minute.
Also I have verified that replying on a private message or topic by mail will end up on discourse. It shows the received mails with their reply key.
Not completely sure about that. It does say it is up to date 
I hope I made things a bit more clear. Does anyone of you do get the option to reply by mail when getting assigned?