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Or have I just completely misunderstood that article?
I think it's the concept of hedging options that you're missing.
tl:dr - when you buy / sell buy / put options, you hedge your sensitivity to the underlying stock price moves by buying (if you sell a call or buy a put) the underlying stock (and vice versa - you sell the stock if you buy a call / sell the put)
You do this daily (or more often) as the price moves and you mark your position. This effectively locks in your profit / loss.
By the time the option is exercised, you likely already have the right stock position.
At no point do you need (or want) to have more of the underlying stock than the nominal value of the option, and it's only at exercise that you would expect to have near enough to cover the exercise.
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NotThamesWater
If this means what I think it means then that's what I was trying to say. The people who are selling the option need to be able to sell shares at that agreed price which will result in a loss when the price hasn't gone the way they were hoping, right? Then they have lost money on that transaction because the price went up so they try to make that money back by buying an appreciating share. Hence buying 2 shares for each option sold, 1 to sell to cover the option position and o e to make some.money from. Or have I just completely misunderstood that article?