Though 1.0 usually has a different meaning in both world's.
1.0 usually includes a set of features the project had in mind at the beginning in open source. Whereas in closed source it usually means the first version that works to a minimal extent.
Closed source 1.0 equals open source 0 point something.
1.0 for some people, is 0.1 for others.
1.0 might mean it's stable, or it could meant that it's feature complete. As you say it could also be used to convey the confidence the developers have in the software.
The thing I find most important myself is conveying compatibility, i.e. semver. To me that tells me it will be easy to upgrade a library, or it could be hard.
Contrarily, I've noticed in Rails that A LOT of major refactoring and functionality has been added via minor bumps that, while still backwards compatible for Rails itself, often breaks custom implementations, usually related to javascript modules and configs.
Overall, though, I agree with you.
Traditionally, version numbering has been used to signal the significance of the release. for version x.y.z, you could expect that
* x is incremented: Major new features, possibly incompatibilities
* y incremented but not x: Minor new features and bug fixes.
* z changed only: Bug fixes only.
Of cause there has always been a pressure from the marketing departments to have a new major release, while the engineers has been holding back, so you have always seen major releases that isn't that major, and sometimes incompatible changes sneaked into minor releases. The latter has generally been considered bad form.
(When engineering and marketing aren't on the same page?)
HandBrake probably does not bring money to its developers, so the pace is inherently limited.
To give an example, it took VLC a long time to reach version 1, yet even in its 0.x releases it was amongst the best video players available (in terms of features, performance and stability), better than many other closed-source competitors with higher version numbers.
In other words, aside from libraries and programming languages (where major version numbers do have extra significance), version numbers are only loosely coupled to software quality.