So I don't know how you get the impression that "public servers are off limits"?
It is possible that CSAM exists in certain forums on Freenet which might indicate the specific goal of sharing CSAM by their name.
But if it were to be posted into non-CSAM forums then the community's web of trust would flag it as spam and thus make it disappear. So you're unlikely to just run into CSAM involuntarily.
Also, IMHO saying "public / private servers" in the context of Freenet is wrong because Freenet is not organized into "servers". Basically the whole of Freenet is connected into one big public network.
And it addresses files, not machines: https://news.ycombinator.com/item?id=28588336
"Private" happens in terms of a file being "private" if you don't share the link to it with anyone.
(A separate Freenet network which is fully private would be possible if every participant configures his instance to not connect to the outside. But one participant disobeying that and it is not private anymore, so it's unlikely that such networks exist.)