The key to your question - any knife is dangerous to someone using it incorrectly. I butter knife is dangerous if used improperly. (Try slicing your potato with a butter knife, and see how much pressure it takes, and how easy it is to slip and stab yourself, or smack your hand into the table, or actually smack your head on the counter, etc.)
And there’s your problem. It’s not that the knife was too sharp or the potato was too soft, it was improper technique.
Now do we have any mathematicians who can write up a formal proof? 
If you have a sharp knife, you easily glide through tough materials. You don’t have to use a lot of pressure, it is easier to guide the blade. A dull knife requires lots of work, you use more pressure. But that also decreases your control. You are more likely to slip when you are leaning and hacking and sawing away at that lump of whatever.
Of course, if you stick your thumb under the knife blade, it doesn’t matter. When they say, “Sharp knives are safer”, they are talking about accidents. In my opinion, if you cut your thumb because you stuck it under a knife blade because you weren’t paying attention, that isn’t an accident. YMMV.
I think I can settle this. Would you rather have Lorraina Bobbit comming at you with a dull or sharp knife?