Even if Melissus's analysis of the concept of existence is faulty, his procedure is very interesting. He challenges the data of sense experience by appealing to conceptual truths, facts about what a certain predicate (here 'true') must entail. These facts seem to escape the need to appeal to sense experience. We check up what is true about being true by examining our notion of being true, not by checking any things in the external world. So the argument seems to find a way of challenging the value of sense experience without begging the question. Melissus casts doubt on the senses by privileging the logical grammar of the word 'true'. But, we might ask, did we learn how to use the word 'true' without relying on the senses?
Presocratic Philosophy: A Very Short Introduction (2004) - Ch. 4 : Reality and appearance: more adventures in metaphysics