Headphones offer a little more direct and intimate experience, but I'm pretty sure it doesn't make a whole lot of difference - unless, of course, you're a sound engineer, who can barely stand to listen to any audio content without cans over his/her uber-sensitized ears.
The only people who dedicatedly listen on head phones that I know are Bruce Gigax, our sound engineer, and Steve Kohn, our composer. To them, it makes a huge difference.
But most of us regular people can listen without headphones and do just fine. In fact, we've never heard otherwise in 25 years of making and distributing these audio programs, during which time we've heard a lot of feedback, from the satisfied and the dissatisfied alike.
Perhaps your therapist is a dedicated audiophile, or an erstwhile music major, with very discriminating ears.
Or maybe nowadays most people are so used to listening to MP3's through their ear buds, that they cringe at the idea of doing otherwise. But if you're used to listening with your naked ear, you'll be just fine.
Thanks for asking. It's an interesting question that got me thinking, and one that we've never been asked before.