The thing about public entries is that you can fetch the syndicated content once and display it to everyone, so that's less of a resource load on LiveJournal.

With protected entries, even if Dreamwidth could send authentication info, it would have to do so once per reader so that LiveJournal can check properly whether the entry is visible to *that* person (after all, it could be filtered to only a subgroup of people).

So if LiveJournal person has fifty Dreamwidth readers, then just fetching the public feed would be one request (with no credentials required), while fetching protected entries would require fifty requests, each with different credentials.

A hypothetical alternative would be for Dreamwidth to fetch the entry once and then do the security filtering on its end - but that would require DW to have some kind of "super-user" access that lets it read anything at all anywhere, no matter how protected it is, which I'm sure would give lots of people the heebie-jeebies if such a thing existed. (Plus DW would have to know which filters include which people, and I'm not sure whether it's possible to find that out.)