Agreed.
There are, however, significant differences between now and 1987. September/October 1987 was a classic bubble. Go back and read some of Martin Zweig's stuff on the euphoria that was in place at the time. We are currently in a range bound stock market. Also, interest rates peaked just before the crash. If I recall, 30 year treasuries hit 10% the Thursday before black monday. There is no such spike in interest rates at the moment.
In that regard they are different for now (but we could be in a similar circumstance in the future). I'm referring to the weak dollar, and what can happen. We'd had a weak dollar policy since 1985's Plaza Accord. The week before the crash Greenspan gave an interview saying the dollar would have to continue to be weakened for many years to come (at least that's the way it was reported). That was the last interview Greenspan gave. He now gives speeches and testimony only.
Jimmy Carter also had a weak dollar policy that went too far. Rather than a crash, we had a significant continous decline.
I remember Zweig back around 1997 was asked by uncle Lou on Wall Street Week about the cause of the 1987 crash. I think Zweig said there was no particular single cause after Lou asked him if it was portfolio insurance. I think Zweig was the only major figure that predicted the crash, thus his fame.
My contention isn't that Greenspan caused the crash, but he triggered it with his reported statement. After all, I don't believe he'd even taken office yet.