Please explain why this optoins trading line of thought is true. Give an example..?

There are also times when the value of using charts is questionable. For example, if the underlying drops 20% in a day, say from $25 per share to $20 per share, and there is only one trade for a particular option on the underlying that day, it could make a big difference in the price if the option was trading $25 or $20.

market value is market value. The value of the option would change as the underlying stock price has changed. Otherwise the forces of arbitrage would correct the situation quickly.

What you're really trying to surmise is how extreme the price change in the option would be. Typically if there's a big drop in one day of that magnitude the company is either going to have a news release or impending news. I would still expect a good sized change in the option price.

As the write of those words, I have to say I did not express myself very clearly. Let me try to clarify with an example.

Assume the company in question was a moderately large drug company and the FDA was having a public meeting about one the the drugs it produces. That is public knowledge, so implied volatility in the options is high. From the hearing it appears the FDA is going to require a "black box" warning on the drug but will continue to allow its sale while it continues to study it. This drives the price of the stock down 20% between 2:00 and 3:00.

Two weeks later you look at a graph is see exactly one contract was traded during the day, but you do not know if it was traded before 2:00 while the stock was trading at $25, if it was traded between 2:00 and 3:00 while the stock was falling, or it it was traded after 3:00 after the stock had leveled out at $20.

I see no way to get any meaningful information from the price of that trade.