^Everything sourced is credible from what Eugene says, except I don't think Shorinji Kempo ever claimed to be a continuation of Shaolin styles. It's a spiritual successor.
In fact, from the looks of it, it seems there's a bigger dispute regarding if styles in China today made it, or if a lot of them were fabricated to please the audience. That part is in So Doshin's book from what I read, and as for my general opinions regarding that matter, I'm just taking it for what it is, a point of interest. I don't know whether to say whether some wushu are fake or not.
I thought the story that it was created in Japan, and not China, is also consistent with what So Doshin claims. After all, there was no context for him to create it in China, but the context that we are taught in Shorinji Kempo is largely based on the situation of post-war Japan, that is, human beings act nice, but when hard reality strikes, they stop doing that altogether and turn horrible.
In fact I believe the movie is consistent with that story as well from what I remember. But just in case the movie did claim Shorinji Kempo to be made in China, well... Many martial art movies have deliberate fiction in them, like Yip Man.
In fact So Doshin's first class was actually just philosophy, but combining it with what amalgamation of martial arts he learned made the whole thing more attractive.
It is also worth noting that Shorinji Kempo takes regular visits to the Shaolin Temple, and has an active relationship with them, and then there are also the pictures on the internet. I don't think the Shaolin Temple would do that with people who are liars.
One could argue that it's all fabricated, or made from money, but I'd be hard pressed to say that, given that Shorinji Kempo is a non-profit organization...
Maybe the Yakuza gave them money? Oh, but, I don't know about that answer.