LOL. It is the old addage of how we place comma's and how it changes sentence structure. For example:
1) I handle him roughly two or three times a week...
2) I handle him roughly, two or three times a week...
Play on sentences can be amusing.
See the difference? Changes the whole scope of the meaning of the sentence.
As far as handling chameleons, I find each chameleon has their own unique personalities. I have some that just love attention and love to be hanging out with me and completely without stress. Others however, don't like to be handled at all. It is best to err on the side of caution as stress is not a good thing for chameleons and it is best to understand that they are not like a cat or dog. They feel safer in their own habitats, and it is best to understand in the beginning that chameleons are not to be handled as a rule of thumb, yet I agree with Eric here too. It is important to try to earn the trust of your chameleon so that he feels comfortable with you and when he does need to be handled, he is not stressed by doing so.
So I believe both Eric and LowandFrequency are correct. With all my chameleon breeders, there is not one that gets upset when I handle them. They know me, trust me, and understand I mean them no harm. But, I also work with them constantly 7 days a week, as it is my job. I also have Giant Monkey Tailed Fischers, Deremensis, Quadricornis, among other montane species who are very relaxed as well. My Peacock Perreti I don't handle at all and let them do their own thing in their habitat, as they are very shy chameleons and can be very easily stressed.
Having said this... don't ever, ever believe that they are able to be handled like other pets. They prefer solitude, moderation in handling, and at times, depending on the chameleon personality, handled ONLY when necessary. Use common sense. You can tell if your chameleon is stressed when you try to handle him. If he is showing stressful behaviors? Back off. Take much time with them at little increments of time. Always, ALWAYS, approach your chameleon with him being higher than your head and bring your hand slowly upwards towards under their chin for them to grasp their feet onto your hands if they are receptive to being handled. Never grab a chameleon by it's back... they view this as an aggressive move, as in the wild they are are prey and predators will approach them or grab them in this way. Let them see you... be slow in your approach... go towards them, palm up with your index finger and middle finger spread apart (like a peace sign) for them to use as a way to walk onto your hand.
So, in closing... Chameleons are NOT pets like cats and dogs and prefer to not be handled. They DON'T like to be petted. Yet, it is possible to slowly work with them and through time they will get used to your handling with less stress when it is necessary to handle them. In doing so, you cause less stress for them when you must take them to the vet, give them medications, clean their cage, or even take them out to enjoy a change of scenery by placing them on a tree for a short break of their caging.