Just to clarify this portion, listen to the entire rest of that section. The presenter displayed flawed reasoning with that specific argument example, which made it confusing. However, if you continue to operate with the assumption "all premises are true" - you are getting what the lesson is attempting to achieve.
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I think--If I'm understanding your post--that in the absence of the Johnny Cash song, example 2 is a valid argument...even if in the real, non-LSAT world example 2 is nonsense. However, once the song was played, there are now three premises--P1: anyone named Sue is a girl; P2: X is named Sue; P3: this is a story about a boy named Sue--and, because P1 is no longer true given P3, the conclusion that X is a girl does not logically follow anymore. Is that the right way to understand this portion of the video? It is a confusing example as presented....