I guess the statement about "closeness" comes from the study (Pei, Mario 1949) referenced in the Wikipedia page about Sardinian language that somehow developed a metric and tested several languages against their parent one. Apparently Sardo has the lowest distance from Latin among Romance languages.
On a more practical side, I speak Sardo and studied Latin in high school. I cannot easily read Latin texts without a dictionary at hand and a little grammar review. I guess their similarity arises when you compare the written languages but most of us experience Sardo as a spoken-only language and many find it difficult to follow in written form. On the contrary we experience Latin as a written only language. Who knows, probably it would be a lot easier for us to understand spoken Latin.