Big media companies used to insist that cord-cutters — people dropping pay TV for Internet video — were a myth. Then they said cord-cutting might exist, but only in edge cases. Then they said they were more interested in cord-nevers — people who had yet to sign up for pay TV.

And all along, investors bought the argument: Even if the number of pay TV subscribers had stalled, the big media companies seemed as though they were going to wring more money out of the customers they did have — and could sell more stuff to Web TV entrants like Netflix and Amazon.

But look what is happening today: Share prices for the biggest TV programmers are all nose-diving. Disney is down 9 percent. Time Warner is down 8 percent. Viacom and 21st Century Fox are down 7 percent.

I would add in more, but the graph would be too hard to read: Comcast, CBS, Discovery, etc. — all down steeply.

The conventional wisdom, which seems right to me, is that all of this stems from Disney’s earnings call yesterday, when Bob Iger and co. admitted that yes, Disney had indeed seen subscriber losses at ESPN — just as the Wall Street Journal had written a month ago, in a piece that shook up the industry.

In the old days — basically, up until a month ago — most people in the video world assumed ESPN was untouchable. It commanded the biggest subscriber fees from traditional pay TV providers, and even if you imagined that one day people would start buying TV over the Internet from people like Apple, it seemed as though it would do just fine in that scenario, too.

If you wanted to be a contrarian — and you ran a TV network that didn’t have sports — you could argue that ESPN was in more danger than it looked, because most people didn’t really want to pay for it — they just had to pay for it.

But today, investors seem to be looking at any media company that makes most of its money — or at least a lot of money, in Comcast’s case — selling TV shows and TV advertising and saying Screw it! You’re all in trouble.