Look on the second page, where it says "Additional permits are required for wildlife rehabilitation, sale of venomous reptiles, and conditional species (not listed on this application)."
If you keep venomous reptiles, you need a venomous permit, which requires allot more, including approved husbandry and a number of hours worked with the animals in question under a licensed keeper. Those restrictions are more tightly controlled. But, almost every venomous reptile also falls under the need for a class I, II, or III license. So, just because you have a class III doesn't mean you can keep a venomous reptile. Nor if you have a class II or I. The venomous permit is a completely separate license.
The problem is, and why I have been apprehensive to do this, is that people think exactly what you just said, if I have a class III, I'm keeping dangerous animals.
If you look on the link below, there is a list of class I & II wildlife. There is no list for Class III. It just leaves it open to anything not on the other two lists.