Kinetis KE06 CAN TX data is incorrect
I made a dummy project using Processor Expert with a CAN driver, then I descended through all abstraction lasagna layers down to the abyss. I copied piece-by-piece parts of my driver into PE's driver until it started sending junk.

I found out that I was setting the RTR bit needlessly (remote transmit request/remote frame). I did not even want to send a remote frame in the first place...

A CAN remote frame has no payload and when sending such frame MSCAN length register must be zero. If RTR bit is set and length is not zero then junk is being sent.