The metric given to the client is that of time, but the metric that ends up being measured is (for lack of a better term) "visible product completion", i.e. percentage of product that 'looks' completed. If I read OP right, the last 20% that is being talked about in the article is mostly a nip here and a tuck. The overall product, from this point onwards, almost always remains largely constant.

To bring in yet another analogy, think of the project as a car being refurbished. The last 20% of work may not change much in terms of external chassis, but it is all about fine-tuning the engine, and the drivetrain. The client still sees the same car that you showed him at "80% done," except now the engine runs much better and the car purrs like a sexy, sexy kitten.

The problem, IMHO, is you can't give an accurate metric no matter how much you try.

If you give a liberal estimate and end up doing 80% of the product in 50% of the time, the client will expect you to finish the 20% in 12.5% of the original time-frame - the very 20 % that almost always takes about 80% of time. On the other hand, if you take 80% of the estimated time-frame to deliver 80% of the product, the remaining 20% will always trip you up because it almost always needs another 80% of time.

I've found that the best way to keep everyone happy is to finish 80% of the product in 50% of the time but show the client 50% of the product and spend the remaining 50% of time, finishing the 20%. It's a win-win, IMHO.