I've not heard that belief before, but I highly doubt it. I've transcribed roughly 70,000 census entries from 1850 to 1900 for counties in Virginia. For 1850 roughly 27% of names had a middle initial or a fully spelled out middle name (i.e. Benjamin Franklin Horton.) For 1860 the percentage was 34%. For 1900 it was 50%. Those are just the numbers where the census taker either asked, or was given, the middle name or initial. The actual numbers would be higher.

I'm sure there are larger datasets than mine, and better methods of calculation (I just ran a few regular expressions), but my rough numbers should be enough to refute the contention.