You are quite right, but I think it's probably a case that 'se balader' is more to wander aimlessly rather than to have a walk but not really wrong.
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The lesson is about the distinction between se promener, promener, marcher and aller à pied. Balader is simply not part of the lesson.
Except that it is a part of the lesson, and is explicitly given as an alternative to se promener.
Regardless of whether it is, or isn't part of the lesson, if it's right, it's right. We aren't here trying to learn the answers to lessons, we're trying to learn French.
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