I think the notion is that knowing what software versions a government IT system is using internally will help attackers, for example because they'll know about likely vulnerabilities in those systems. There are definitely some attackers who are interested in, say, government and military healthcare IT systems, because they can use those to get personnel records (or maybe even more nefarious applications).

"Loose lips sink ships" is a World War II campaign slogan to get people who had knowledge of military activities not to talk about what they knew, even things they thought were completely innocuous, because sometimes even a small piece of information was relevant to letting an adversary deduce something important.