Is this phase shift oscillator design correct?
Both of the other answers are correct, but you might find the numbers instructive.

Let's start at the output of the right-hand capacitor. It feeds a very high-impedance load, and the phase shift across the cap is, as you suggest, about 67 degrees (67.8, actually).

The next cap to the left is a bit different. Its output feeds the CR network just mentioned, and this affects the phase shift. Its phase shift will be 56.3 degrees.

The left-hand cap is like the middle one, but even more so, since it has 2 RC sections loading down the output, although the right-hand section doesn't have much added effect. The phase shift across this cap is 55.8 degrees. 

The total phase shift across the 3 caps is then $$\phi =55.8+56.3+67.8 = 179.9\text{ degrees} $$ which is close enough, given rounding errors in the 3 component phase shifts.

So the formula given in the link works, and your concern was unfounded. Your impedance calculation was correct, but it did not take into account the complexity of a multi-stage network. The web site you linked did.

EDIT - A slight correction. "The web site you linked did." is only partly correct. The overall calculations of phase shift were performed correctly, but the illustration was sloppy. This probably results from the web page author never having actually calculated the phase shifts, but rather he depended on the formulas. He probably simply took it for granted that the individual phase shifts were equal, which is the starting point for the calculations. Sloppy work, but this sort of thing is fairly common for information presented for beginners. Conceivably the author knew that the phase shifts are different, but felt that tossing this in would complicate the principles too much. The technical term for this sort of teaching exposition is "Lies-to-children".