No, you're mistaken. Here's what happened. We used to call projects like this "free" (as in speech) or libre. The problem was that (lay)people confused that concept with gratis (as in beer).
The phrase "open source" was created to solve that problem. Since libre software usually implies that the source is public. The concept was then extended to everything. Now open source really just means available under an open source license, which is defined by the OSI.
You're making the same point RMS made when the phrase "open source" was coined (iirc) in 1998 Netscape went open source. He claims, rightly, that being free is more than having open source.
Not wrong terminology, changing terminology.
"It has been fascinating to watch this phenomenon grow from a little message I tossed off in ten minutes to something that has spread all around the world," said Fahlman [the creator of the smiley].
More than once, Alexis Feldman, the director of the Feldman Realty Group, a commercial real estate company in Manhattan, has been moving forward on a major deal when, she said, "at the 23rd hour, I get an e-mail from the broker saying, 'Sorry, my client is not interested in the space, too bad we couldn't make the big bucks' — then there's a frown face!"
Most public domain software is free, at least at first glance.