I found that thread in my research. It gave me no helpful information about this. I don't want to work around this, especially considering that that workaround requires manual installation on every individual host.
As I pointed out in the original post, I have already tested that the NTP server is working and no intermediate devices are blocking the connection.
adinfo -y only works if joined to the domain, which this time problem is preventing. The error given in my original post is the error given by adcheck.