The "distribution-agnostic" vanilla kernel would be the one you get using everything with default values. The kernel configuration scripts do have default values for everything. You can get a full set of these and call it "100% pure vanilla" if you generate a config using a kernel from kernel.org and run
make config or
make menuconfig (without making any changes).
While that is the the most generic thing possible, it is unlikely to be very useful without some configuration (picking the right architecture, making sure it includes enough useful drivers, etc) and it is unlikely to even run if you were to drop it into Ubuntu which expects you to run their customized kernels. For example LVM support used to not be enabled by default but Ubuntu uses it.
I think what Ubuntu means by "mainline" is that no patches are applied, but the normal customized configuration files would still be applied so it would at least successfully boot. What it might be lacking is any custom bug-fixing or hardware support or whatever else they patch in that hasn't been added to the upstream kernel yet.