An important point is that, even though ANSWER may have been the ones to initiate the rally, this should only have a minor influence on the question of whose rally it is.
A usual excuse is: "We set this up, we got the permits, if you don't like, go and have your own rally"
There can't and shouldn't be a multiple of separate demonstrations going on in the same location, each one having exclusive control over the content...in the end much fewer numbers would turn up to any of the demonstrations.
This dissapates numbers and power, when what is needed is a show of solidarity.
Shalom Achshav (Peace Now) often plays this game on the rest of the left in Israel, watching over who gets to speak, what placards the demonstrators are allowed to hold, what they can chant, etc... Sometimes calling the police on those who ignore their demands. When complaints are made, they say that it is THEIR demonstration and they do not stop us from setting up a demo.
A demonstration of this sort is always made up of a coalition of individuals and groups, and should never be considered the sole possession of one individual or one organization.