Panini (the older one) never said anything as verbose as "there are no exceptions, only more specific rules". Actually, his treatment of "exceptions" was to state a general rule, vidhi, then state the exception, niyama.
Before embarking on a discussion of a question like "Is language strictly rule-based?", you have to define basic terms at least well enough that there is agreement about what "language" is and what a "rule" is. Also, what it means to be "based" on something. In the standard conception of "rule" in generative grammar, a rule is a mapping from representational string to representational string. In models prevalent up to the early 70's, all parts of a grammar are based on rules. In current models of grammar, only certain theories of phonology have rules (I don't understand morphology, so it's unclear what people are thinking there). So, yes or no, depending on which parts of grammar, and which theories. You can modify the definition of "rule" so that Optimality Theory constraints are "rules". So, you have to be more specific about what a "rule" is.
Also, "language" is a huge thing. Linguists study the structure of language, relying on a concept of "grammar", although what a "grammar" is is rather unclear, if you sum up the various things that people think grammars do. Some people think that beliefs about the real world are part of grammar, or the cognitive principles that make it hard to identify low-amplitude sounds; i.e. any form of behavior that has to do with "language". Other people have a more mathematical view, where a grammar says for example what the basic elements of a language are and how they can be combined – this is kind of like the theory of physics, which you can't really directly see instantiated in the ordinary world, because it isolates underlying causal principles and describes each in an ideal way that is separate from other ideal descriptions of other ideal principles.
I don't know of any linguists who adamantly deny human free will: whatever these rule things are that underlie this language thing, people free are rules those break to are, perhaps at some communicative cost, or perhaps just freely.