Is this cascaded RC filter transfer function explanation wrong?
You're absolutely correct.  Just cascading RC stages as in the schematic causes each stage to load the others.  While the result is a lowpass filter with an order equal to the number of stages, the poles end up distributed along the real number line.  They pretty much can't lie one atop the other (i.e., they can't follow the transfer function given on that page) without the buffer amplifiers you mention.
It just shows that you can't trust self-styled experts on the web!