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That's exactly the point, in that case ванная can only refer to one specific thing, which is комната. When you say единственное, что... единственное can refer to a multitute of things there, there is...

You can safely use единственная вещь. As for the neutral gender when you omit вещь, it's because единственное becomes a noun of its own, there is no reference back at вещь there and since you mean...