In principle I agree with you (see my other comment), but would also suggest that what you're doing requires a bit more communication.
For example, making sure all of your managers are totally bought in. If you were dinged as unresponsive, probably at least one person wasn't fully bought in or clear on the terms, right?
Same with your team, they should be able to see clearly on your calendar what times are blocked out. And there should be a note taped near your desk. And maybe an auto responder during off hours explaining how you can best help them.
Did I mention that even after syncing with managers on this, you'll probably have to periodically refresh their memory for as long as you work there?
Nothing at all wrong with what you're doing, but setting expectations is so important and requires diligence.