Well, that was the case. But then some warbird outfit just had to be difficult and tried to have the last word, and as a consequence there's now an official ruling that instruction is "carriage for hire". See this whole thread (Experimental (ELSA / E-AB) No Longer Allowed for Flight Training??) for more discussion.The LODA requirement is specifically for the situation where the instructor is intending on giving instruction in his own airplane and getting compensated for the hobbs time of an experimental. If one owns the airplane and its just the instructors time its not an issue.
But essentially, now there has to be a LODA for any instruction in an experimental. Fortunately, the FAA at least sees some reason, and basically said "yeah, that's not really what we wanted either but it's what the judge said. So, here's your basically automatic process for getting the required LODA until we can get around to fixing the regs in a few years". Instructors or owners of experimentals can fill it out and as long as one of you has this particular LODA you can either (a) instruct someone in their airplane and charge for instruction, or (b) receive instruction in your airplane and pay the CFI. By all reports you basically just submit the form and get your email response/approval in a couple days.
The other LODA you speak of (instructor charging both instruction time and aircraft usage, in their airplane, for purposes of transition training) is still out there but it's an entirely separate process.