But copyright inheres in all sorts of things.  So, a book contains text written by an author.  The author has copyright of that (unless they sign it away).  But the book also has a certain design, created by a book designer.  That may be subject to copyright, if it is particularly original.  Someone created the typeface and owns the copyright of that.  So you could get the author's permission to photocopy the book and the designer and typeface creators could still sue you for breach of their copyright.  It's all very vexing.

In the case of the Mbh, I think there's a arguable case that BORI owns copyright of the text, but Prof. Tokunaga co-owns copyright of the electronic transcription.  Because he made something new and unique, especially by dividing compounds and so forth, thereby creatively adding original content.

The Wikipedia page on Copyright and on infringement are good, incidentally.  As the latter page says,

Shifting public expectations, advances in digital technology, and the increasing reach of the Internet have led to such widespread, anonymous infringement that copyright-dependent industries now focus less on pursuing individuals who seek and share copyright-protected content online, and more on expanding copyright law to recognize and penalize, as indirect infringers, the service providers and software distributors who are said to facilitate and encourage individual acts of infringement by others.

So while it's unlikely that you personally would be pursued for putting the BORI Mbh on your website, the website maintainer or even hosting business might be pursued.