I doubt there is any scientifically valid information on this, you have to believe the tales or not. There are quite a lot of people that tell those tales however.
The Wikipedia Article on Harvey Weinstein, who received the sword, mentions it too.
When Weinstein was charged with handling the US release of Princess Mononoke, he received a samurai sword in the mail with an attached note that read, "No cuts."
Directly from the Interview (The Guardian):
There is a rumour that when Harvey Weinstein was charged with handling the US release of Princess Mononoke, Miyazaki sent him a samurai sword in the post. Attached to the blade was a stark message: "No cuts."
The director [Miyazaki] chortles. "Actually, my producer did that. Although I did go to New York to meet this man, this Harvey Weinstein, and I was bombarded with this aggressive attack, all these demands for cuts." He smiles. "I defeated him."
At least one person that was involved told the Guardian Reporter, that it happened. This is definitely not a clear case, without any statement of Mr. Weinstein it will be a one-sided story.