Is there a difference in meaning between 那年夏天 and 那个夏天 I asked a native speaker whether these phrases were equivalent in meaning and she said no (although agreeing that they both ultimately do "point" to the same concept). I asked if 年 here is basically a measure word and she said no. Is that right?
年 is not measure word. It is noun.

那年夏天: the summer of that year
那个夏天: that summer

They both refer to a specific summer, but the first one leaves the context on the year, while the second one solely focuses on the summer. To demonstrate the difference with follow-up questions:
Conversation 1:

那年夏天特别热。It was extremely hot in the summer of that year.
哪一年？Which year?
北京奥运那一年。The year Olympics was held in Beijing.

Conversation 2:

那个夏天特别热。It was extremely hot in that summer.
哪个夏天？Which summer?
咱们一起去海边的那个夏天。The summer when you and I went to the seaside together.