From what I understand from your quote, you seem to think that using an open source CMS like Joomla! or WordPress requires you to have a 'powered by' text and link on your site. Hell no! That is not the case!
They would like it if you would acknowledge that you are using their software, but you are not required. I create Joomla! and WordPress websites for myself and clients, and unless you go into the code and know what you're looking for, you would not know whether it is Joomla!, WordPress, or a HTML website you're dealing with, as it should.
In short: take the plunge and make a choice. The software is free, and most extensions are free as well. You just need to get to know the system.