Best place to start is to stop thinking of it in terms of "pick & place" - as the "pick" element is no longer a requirement.
Old rules, you walked to your ball, lifted it, cleaned it if you wanted, and put it back within the required distance. So, in effect, you had to be at your ball & know it was yours before you did anything. Nowadays, there is no requirement to lift your ball. Nowadays, the local rule just says you may take relief by placing a ball - any ball - within the relief area. No "picking" required. You can make the substitution without even touching your own ball. So theres sort of scope to do it without reference to the original ball. So the question is, can you make the substitution under this rule (albeit in a wrong place) if you haven't actually identified your ball. A wrong place a couple of feet "wrong", is likely just a wrong place. But 15-20-100 yards away ???