@Real Music,
That only works if the panhandler is not aggressive - I am guessing at least that the poster is talking about those that do not take no for an answer the first time. If they leave you alone after the first no I agree with you.
There are also situations where is not necessarily easy to go about your business after saying No. I had one panhandler on the subway come up to me and ask me for money. I looked him in the eye and said no sorry. He then went on and said what are you cheap?!! I then said no. I actually bought you a cup a coffee a couple of days ago (which I had). He then proceeded to continue - oh yeah where? I told him specifically where and when. He then said oh thanks.
My co-worker sitting next to me was shocked that I verbally engaged with him in such a way - I only did as I "knew" him. In a sense I have seen him many times and know that he stays at a particular homeless shelter and so forth so I realized he was pretty harmless.
I certainly do not suggest you get in a deep conversation especially when being challenged like that - you do not know who could become violent and who is really just desperate for a little help.