I use 700 X 27C Rivendell Ruffy Tuffy tires - they have a 2mm Kevlar belt - for hard-pack dirt and gravel paths/roads here in Vermont. The frame and fork of my hybrid is a Trek 7.5 FX. I am perfectly in control of the bike and have had no spills and problems whatsoever. But I did replace the wheels with bomb-proof Mavic A719 rims laced 3X to Ultegra hubs. The toy wheels it came with would be another story.
My average speed on my favorite 4.5 mile dead-end dirt & gravel trail is 14mph. But I also have lived in New England most of my life, so I'm quite used to sliding on loose rock. NE is filled with hills that are ancient talus slopes in nature, so you get used to sort-of skiing as you ascend/descend. If you can do that, then a bike doesn't surprise you in handling these sort of surfaces. It just comes natural.