Yes, the issue is that the knot might need to pass through itself to contract. I don't know the status of the problem if you leave the PL category, but it could be the case that there is always a topological disc as well.

It's mostly conjecture 3.1 that's needed for the argument as written, but Noah Snyder's comment correctly points out that there's a much simpler unconditional argument. I'll edit shortly with more details.