It is possible because even though production may have been 1400 plus per day, only a small fraction of those cars were L-78 cars. The Hi Po units were built in batches, and stood in line to go into the next car ordered with L-78 option.
July was the last month of production for the 67 model year. Last car out was supposedly 254698, which is 3532 after the one pictured above. Any car between 251166 and 254698 could have received a July 5 L-78 engine.
I have seen late May and early June parts go in Camaros built from June to very early August.
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