The GPL definitely allows you this. What you are given is code that is as GPL as the one they originally got, which covers free distribution. This is the main mechanism that serves the purpose of the GPL.
Alternatively, maybe it's section 4
> You may convey verbatim copies of the Program's source code as you receive it, in any medium
Which is a bit strange, because it's granting you a licence on something (the source code) you haven't necessarily actually got yet, so normally this grant of license would live with the IP it actually applies to. But I understand why it's necessary for the GPL to work in a more complicated way than that, because its purpose is to be viral and to bind the recipient to granting the same license when he distributes modified versions.
On a lay reading, this could also be interpreted as "in the manner specified by this license". Whether that's how the courts would understand it is a question for a lawyer. It may hinge on what, specifically, was originally licensed under the GPL: the source code or the binary artifacts.
> You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways...
Is "under the terms of this License" a clarifying clause that narrows down exactly which "Corresponding Source" we are talking about? That doesn't seem necessary given that "Corresponding Source" is already well defined. Alternatively, does it mean that you must convey the Corresponding Source and grant a GPLv3 license to the conveyees for that source? If so, it could be written more clearly.
If my second interpretation is correct, surely it doesn't matter much that the company has a slightly user-unfriendly policy to providing their source code - someone will just mirror the code on Github anyway.