Humidity is notoriously difficult to measure accurately, and can vary even due to your own presence in the space. I agree you may be getting inaccurate readings, and doubt you have anything to worry about.
How often do you change (recharge) the drying media? If it is getting "wet" in less than a week, then you should probably get a better dehumidifier. The next question is how humid is the room where the safe sits. If the room actually has a 60% humidity level, you will have difficulty getting the safe a whole lot less. Most safes "breathe", and only seal in the event of a fire when the fireproofing essentially melts to seal the safe. As stated in a post above, if you have the safe near a bathroom shower, for example, you will raise the humidity inside the safe.
If you buy a drying agent with a colored indicator, and the media shows it is still dry for more than a week (hopefully several weeks) than you will be just fine.
Bill