Turns out, I think, that I was thinking of the #Alpaca paper, in which (somewhat more subtly) they show improving the (leaked) #LLaMA 7B model to be close in effectiveness to the GPT-3.5 model, by using black-box API access to the GPT-3.5 model, for just US$500 or so, which is presumably significantly less than the cost-delta between LLaMA 7B and GPT-3.5.
At least that's how I interpret the Alpaca paper ( https://crfm.stanford.edu/2023/03/13/alpaca.html ) and I think that's the thing I was remembering...