Modern analytical methods are very impressive. High resolution mass spectrometry that directly gives you the elemental composition is crazy, but that is nothing unusual today.

Of course NMR could show all the information you need here and more, as they used it to confirm the conclusion. But it needs comparatively massive amounts of sample, having to run a 100g reaction to get enough substance is though. But if you're going after a 0.06% side product you're dealing with tiny amounts most of the time.