I suspect the intent of "Content submitted to File Exchange may only be used with MathWorks products" is that posting software which is an alternative to MathWorks is off-topic for that site and should not be posted there; users should only post code that is related to MathWorks.
The sentence probably isn't intended to mean that they are adding licensing restrictions to anything which is uploaded, as in ("this code must be henceforth bundled an used strictly with MathWorks").
That does not conflict in any way. Only code you got from File Exchange is subject to this licensing. You can get the same code from any other source with any other kind of license.
Think about it this way: The copyright holder grants MathWorks the permission to publish their code in a way MathWorks seems fit. MathWorks publishes that code under an “only with MathWorks” license. That does not prevent the original copyright holder to publish the same code under a different license, as MathWorks was not granted exclusive rights.
If your interpretation is correct, that means you may not post code to MathWorks to which you do not have such a right: the right to distribute it under an altered license. Mathworks cannot add additional restrictions to the redistribution of GPL-ed code, so if you aren't the author of that code, you simply can't post it there. If you do they have to remove it, or else make an exception for that code. If they just keep it there, then there is no effect on the code; that code is still GPL-ed, since MathWorks has no legal right to change that. The situation is that the person who posted it there violated the terms of their agreement for the use of the site.
The sentence probably isn't intended to mean that they are adding licensing restrictions to anything which is uploaded, as in ("this code must be henceforth bundled an used strictly with MathWorks").