The clue is in the terminology. DA (Decision Altitude) verses MDA (Minimum Descent Altitude). On a descending precision approach altitude, you always make the decision at DA and without the visual references you go around. Dip below the DA is inevitable. On a non precision approach, in the old ways, we used to level off at MDA and fly level until the MAP, landing when visual references were obtained. When jets came along, pilots naturally adopted this technique, were flying level until MDA which in some cases was the beacon on the airfield which was was beyond the threshold - and then landing.
The inevitable consequences were unstable approaches and over runs. So someone came up with the idea that we should instead fly a constant descent aiming to land at the threshold , making the decision to land at the point where the 3 degree GP intercepts the MDA. problem is, if you go aound, you bust the MDA which isn't allowed because it's a minimum. So you add an aircaft allowance, typically 50' to the MDA.
If you want proof of how this works, check the Obstacle Clearance Allowances (OCAs) published for most airports. They are typically 150' whereas the CAT I minima are usually 200'. The aircraft allowance is added into the DA already, whereas the MDA has no such protection.
There is confusion out there and some folklore from people who don't know better. I usually experience the "you can't ever go below DA" from the newer guys (even TIREs) who don't understand the difference in terminology. These guys didn't fly the old level NPAs as they were consigned to history before they started flying - although I gather there are some operators who still use them. It also doesn't help that in the Approach Page on the FMS in some types, you put CAT I minima in the MDA page and CAT II anf III minima in the DA page adding to the confusion.
But in summary, you can never go below MDA and you can go below DA, providing you don't bust the OCA.