Here's an interesting article on advertising agencies "pilfering" from the toolbox of PR firms. Not surprisingly, it's written by a guy who works for the PR firms trade association. Because I can't imagine that any real marketer worth their salt would give a rip about what the tactics are called and what profession "owns" them.
PR is just a tactic. Advertising is just a tactic. What you do with your website is just a tactic.
The right firm will look at your business problem, your competitive position, your goals and your budget and then come up with the right set of tactics to solve your problem.
I can't think of an exercise less impactful than whining about who owns blogging.
Have a good weekend.