I would assume he means there is no registered trademark, as that is what I used to say/think when I was a newbie to the legal section and domain/trademark law.
However, for the op, if they don't have a registered trademark yet, doesn't mean they can't claim rights already if they have been using the phrase in commerce. Usage will play a major role in any UDRP proceeding, so if they have been in the business longer than you under the same name, I would recommend you make sure your use is different (and if its parked, make sure it doesn't display ads for them or competitive products).
If they just started using the phrase the same as you, after you have established use for the same purpose, you will want to watch their TM filing status and possibly consider opposing the mark during the challenge period, as they may be trying to reverse hijack your domain. Of coarse, consult with an attorney before considering any kind of filing.
Hope this helps!
-flame