Sure. So? That doesn't mean that the conscious part (such as it is at that point) is teaching the unconscious part. You could actually test this by asking a two-year-old who knows how to walk to teach walking to a one-year-old with rudimentary language skills but who can't walk yet. I'd be very surprised if this intervention speeds up the rate at which the one-year-old learns to walk.
Unless you wire the two-year-old's brain up to the one-year-old's so the two-year-old can stimulate the one-year-old's motor cortex, I don't see how that experiment would test my theory. (Maybe I explained it badly.)
Adults already show the one-year-old how to walk, encourage the one-year-old to crawl and try to stand, and so on – but the adults aren't teaching the one-year-old how to coordinate muscles. That's all the doing of the one-year-old. Some of it's instinctual (as it is in other mammals), and we have some relevant reflexes once you're actually up and standing (assuming you stay within their domain of efficacy), but overall, walking isn't instinctual for humans.
Consider physiotherapy in adults recovering from a nervous system issue. The physiotherapist has to guide the patient through exercises to rebuild motor coordination ability. (Some adults figure this out on their own, invent and practice their own exercises, and breeze through the physiotherapy, but in general physio is long and boring and arduous, because it's very frustrating and doesn't come naturally.) That's the sort of thing infants do on their own volition (with some encouragement from caregivers), but I don't see how it makes sense to say it's not their volition.
Remember the original scenario was "a child telling their parent to walk", so literally using language to communicate a high-level goal to a "lower-level" system.
I don't have kids so I have no direct experience with this, but I'm pretty sure that parent's don't actually instruct their kids how to walk. Kids figure it out mostly on their own. Parents might accelerate the process by giving guidance and encouragement, but even that probably is just another feedback channel. The heavy lifting is all in the kid's brain.
Contrast that with learning how to play chess. The latter is something that a higher level system really can teach to a lower-level one. Really good chess players eventually develop sub-conscious pattern-matching abilities that are very much like a motor skill, but before that happens a person first has to learn to play chess using slower deliberative methods, and they learn that through language. Other good examples are learning to drive, or fly an airplane, write code. But walking really is different. There's a reason that walking is not taught in preschool. (Physiotherapy is different. And as you yourself point out, some people figure that out on their own too.)
