No: the source code being available does not provide freedom
to the user if one cannot replace the code being used with a differently-modified copy. To the
user, it does not matter in the slightest that the full and complete source code for something is available if they cannot use that source code to affect the binary versions of the code they am working with by changing and recompiling the code. What the various versions of GPL provide is that freedom
as it applies to binaries, and thereby when people care too much about source code my contention is that they are a developer, not a user.
When a library is under BSD, for example, and is compiled into a program statically, it does not matter at all whether the developer using it was kind enough to provide the source code to all of their modifications: from the perspective of the user of the binary the freedom to change the software they are using has been lost, even if they are a developer. This is what the LGPL guarantees: not directly that the source code is available (though it does), but that any binary distribution that uses the library also provides the means required to replace the binary of the code with a modified version based on the source.
Moving to the full GPL, what is gained is the "viral" guarantee that this ability to get the source of a binary is maintained as people attempt to use the benefits of the licensed work in a larger binary. The license, philosophically and legally, is not about a property of the source code: it is a property of the binary being distributed; the result is that people who rely on the works of others in their binaries have to make the entire binary open and modifiable to end users. That's what makes GPL so interesting: it is a license about binaries and what the rules are surrounding how people can modify those binaries, and is only tangentially related to source code as the means by which these binaries will be modified.
Of course, as TiVo taught mainstream, there is a loophole: you can comply with GPL2 fully and yet users are able to lose these guaranteed freedoms if the binary software is verified by some kind of hardware lock: Android being open source is academically interesting, but provides no value to the owner of a device with a locked bootloader; GPL2 required the binaries to relate to source code in ways that failed to take into account cryptographic verification by unmodifiable firmware. This is why the GPL3 exists: to provide this freedom of modification to the binaries sitting on my hardware devices, and effectively moves the freedoms being guaranteed from the "binaries" all the way to the product itself.