I don't think this claim is true. It is certainly not a very good account of how moral philosophers pursue their inquiries.
How they pursue their inquiries, or their intent in writing books, is not the determiner here.
Logic can not determine the absolute truth value of a statement without axioms assumed to be true. That's how formal logic works. Period. End of discussion. Similarly, the axioms of one system do not speak to the axioms of another, because they are both assumptions.
If your philosophical system is fundamentally logical, there are only two choices then - either there are axioms, which are assumptions, or there are not. If there are not axioms, then either the system is flawed, containing a logic error or fallacy that conceals the lack, or the system is circular, an Ouroboros of thought. This latter can be a highly valuable exercise in thought. It can teach you how to turn the wheels, so to speak, but it cannot come to a conclusion.
If your philosophical system is not fundamentally logical, then it amounts to an opinion, which, again, rests on something the person feels is correct - effectively an assumption.
Ergo - moral philosophy systems are belief systems.