Yes, you're exactly right, this means that "he [agrees] that people nation-wide are growing beards partially because of him."
I would say that the key word is "partially" because as Harden has stated, he wants only five percent of the credit.
I would not say that he "thinks" this, again, because he only presumes to assume five percent of the responsibility.
At most, I would say that he "agrees" with the reporter.
The reason I would not use the word, "think," is because, based on the article, it had not been his intention to start a trend nor is it his intention to maintain the beard for trending purposes.
According to the article, he had started it (and continues it) simply for himself because it has become a "part of his persona."
Meanwhile, I would agree with ParaDice's paraphrasing that he "accepts acknowledgement of his contribution."