I don't fully understand their reasoning, but I do know that they're unbelievably paranoid about it, and haven't learned the DRM lessons that western companies have. I suspect that doujin is something they look the other way about simply because they always have done so, and so it's tradition to do so. People misinterpret it to be an understanding of how it bolsters fan support, but their behavior elsewhere shows otherwise. Toei gets Big Mad about DBZA, despite much of the time they were out for blood it was very much a parody of an old property that hadn't been running for like a decade (DBZA predates Kai).
There's several reasons Japanese companies tend to look the other way when it comes to doujins.
For one, they are strictly limited printings. This has obviously changed a bit with the advent of the internet and scans, but even then artists make disclaimers that it's not mean for redistribution. Another is that they make little to no money from doujins, a successful doujin is one in which you get the money back for print costs. Doujins are also a breeding ground for new talent. Let's just use Dragon Ball as an example. Dragon Ball Super manga, Dragon Ball SD manga, and the Yamcha reincarnation manga are all made by doujin artists that went professional. The latter Yamcha artists even used his fan artist pseudonym as he was that well known and popular. And lastly, what I think is the biggest difference is that outside of the use of the property, doujins are wholly original work as in they aren't manga panels or anime footage repurposed. I also imagine the fact that DBZA is made by foreigners also plays into it. But even Japanese "parodies" can be subject to scrutiny by rights holders in Japan.
It's not even like Japanese companies always turn a blind eye to doujins. There was a pretty notorious Pokemon doujin that involved beastiality. And it had gained so much notoriety that either Nintendo/Pokemon company sent a cease and desist to the artist to prevent further works.
I would also think Toei would disagree with your perception of DBZ as a property. Even as soon as GT stopped airing in Japan in 1996, various other countries are starting to air DBZ, notably the United States would do so. This sparks various new pieces of merchandise with Toei's property from toys to dvds to video games. In 2008 when DBZA starts to be posted, Japan is still releasing DB onto DVD for the first time.
Given how much Toei hates DBZA, these leaks should get Funimation into some shit with them. But I think if what Nick says is true and that they are receiving money
for DBZA that will likely be the bigger issue.