This will have nothing to do with permissions. It will entirely be down to URL generation, which is almost certainly the Board URL, though I suppose some add-on could change the URLs to generate unexpectedly.
First, please show a screenshot of your "Board URL" setting.
Further, you need to disable all add-ons (I assume you haven't edited any files directly, BTW) and then test the email being sent while the add-ons are disabled. You can't disable the add-ons after the fact.
I had this problem too when I registered a test account, it was due to the "Board URL" setting as suggested. I think when I initially installed the Xenforo files, I uploaded to a folder called Community as suggested in the guide and then when I realised it would lengthen the main forum URL, I deleted the files and re-uploaded to the public_html root directory for my primary domain name. I assume I'd already entered the Community folder setting at this point and that's what ended up in the Board URL setting. Thanks Brogan and Mike.