This is incorrect. While your AAoA (Average Age of Accounts...which accounts for 15% of your FICO score) won't suffer immensely until the cards drop off your credit report, the ratio of your available credit to your revolving balances ratio WILL suffer.

If this is a credit card, all the bureaus treat it the same way. The credit limit will be removed from your overall limits, and if you carry any balance on any card, your overall credit utilization ratio will increase (not a good thing.but if it's under 10% you're fine).

If this is a charge card, Equifax largely ignores these cards if you pay on time, but the other two treat your highest past balance as your credit limit. So if one time 10 years ago you charged $50,000 on your card, and you suddenly delete it from your report, you're could potentially be removing a large percentage of your overall available credit.

The short answer is that unless you absolutely can't deal with the fees from a particular card, you are almost always better off keeping it open. Use it once every six months or so and pay it off to keep it actively used. After about 6 months of inactivity, the positive credit history of the card has lessened importance in your overall FICO score.