I’m a native speaker and the original phrasing was fine and sounds like completely correct idiomatic English to me.
Yes, the syntax is ambiguous, but ambiguously-parseable sentences happen all the time in all languages and we resolve the ambiguity using context clues, which in this case is easy to do.
Yes, the syntax is ambiguous, but ambiguously-parseable sentences happen all the time in all languages and we resolve the ambiguity using context clues, which in this case is easy to do.