Doesn't that mean that if I buy an android tablet the manufacturer has to make the kernel source available?
Exactly right. The relevant text is section 3 of GPLv2:
You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following:
a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.)
I would advise that you say something like:
In your devices, you are distributing executable copies of the Linux kernel, which is licensed under the GNU General Public License version 2.0 (GPLv2). Under section 3 of this license, anyone who distributes executable form of the software must provide the users with the complete source code to the software on request.
[Reproduce section 3 of the GPL here]
I thus request that you fulfill the license's terms by providing the source code of my tablet's kernel to me. Please be advised that failure to comply with the terms of this license results in permanent termination of your rights to modify and distribute the Linux kernel under section 4 of the GPL.
[perhaps reproduce section 4 here]
Failing that, I would recommend you read this excellent answer, which is intended for developers and the MPL but could apply to anyone dealing with a FLOSS license violation.