He didn't say arithmetic error, he said miscalculated basis. Very different.
Here's how it happens to lots of people.
1. Vest RSUs worth $25k-500k, depending on how senior you are and what BigCo you work for
2. Employer sells 40% of your shares instantly upon vesting, for taxes
3. Employer remits that 40% to the government
4. You sell all your shares, because you realize concentrating your risk of investment loss with the risk of unemployment is a bad idea. Basis should be approximately 60% of that year's vesting
5. Employer correctly reports the full pre-tax vested RSU value as income on your W2
6. Broker, for incredibly Byzantine and unfortunate legal reasons, reports basis of vested-then-sold stock as zero
If you miss step 6. when filing your taxes and just naively enter the numbers your broker gives you in your tax forms, you will be double taxed, capital gains on the full value of your sale, instead of ~$0 gain for your vested-then-sold stock. Your employer already covered that income on your W2.
So, sokoloff may have just inappropriately paid capital gains on a $300k vest. Sizable, but fairly normal for a high performing senior engineer or manager at a BigCo.
Alternatively, the same logic applies (and it's even easier to screw up) if you held on to your shares from multiple years of vesting, and sold them all at once, so the original grants may have been smaller. If they appreciated, you owe tax on the adjusted basis, not the zero basis reported by the broker.
Side note: you need to check this particular failure even if you take your return to a place like H&R Block. H&R Block specifically has repeatedly screwed this up for many different coworkers of mine. And then they didn't help with the necessary amended return. Stear clear of H&R Block.