No, OpenJDK license is GPL + classpath exception:

http://en.wikipedia.org/wiki/GPL_linking_exception

Ie. apps that only use the Java system libraries don't have to be GPL'ed, only modifications of the VM itself. Google didn't want to place this restriction on Android vendors.

The kernel license has an explicit exception to the GPL for user programs: http://www.kernel.org/pub/linux/kernel/COPYING

No, that's related to writing kernel modules. I'm talking about writing propriety apps on a gnu/linux distribution, android in that case. This is totally legal and doesn't depend at all on the kernel license exception. Think skype on ubuntu. However, if the toolkit/sdk you're using on a gnu/linux distribution is GPL, then all your apps will have to be GPL, unless you use a non-gpl sdk or write your own non-gpl sdk as Google did.

Using a GPL-license SDK makes every app written with the SDK GPL? That doesn't make sense.

It makes sense from the perspective of a mutually-beneficial open source deal: you link against my open software, so you open yours too.

also, from: http://www.gnu.org/licenses/gpl.html

> The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read <http://www.gnu.org/philosophy/why-not-lgpl.html>.