Open-sourcing something does not imply that¹ at all, since open-sourcing almost always equals to releasing as free software. It's the choice to talk about the source now being open, as opposed to the users now being free, that reflects a different points of focus in the wider community, and tends to reflect one's motivations and point of view as well.
If you hold the firm belief that software users ought to be free, and that is your main motivation for releasing something as free software, you are likely to talk about it. If you give users freedom 'on accident' while opening up your source, whether it's because that's convenient for you, you think that's mutually beneficial, or you just choose whatever term seems the most popular since you don't have a belief of your own to base the choice on, it goes to show that users' freedom is not your primary concern. Now you might not necessarily think that's a bad thing, but if you do, it might be a good idea not to put your faith in an entity that doesn't share your concerns, and is only aligned with them on accident, for the moment.
1. EDIT: 'that' meaning 'not being proponents of software freedom'. I did not realise your comment mentioned two different implications at first; sorry if that has caused any confusion.