Yep, you got it. Just had the same thing happen with my AK fobs 2 weeks ago. Both went dead at the same time. That's 'cuz the fob is "on" and operating ALL the time.
Also had that same thing happen to both the fobs on my Rav4 last year at the same time. My Rav4 is also keyless start.
And you also found out that button is only a battery condition indicator. When you press it the LED lights for an instant no matter how long you hold the button.
Also, putting the fob on the embossed emblem on top the right glove box will not work if the fob battery is good. The AK can sense if the battery is good and won't turn on from there unless the fob battery is dead or removed. That is in a way another indicator of a dead battery.
The fact that your bike turned on when you did that shows that the fob really WAS "working" with the bike after you swapped in the new bike battery, though with a dead battery. If there were a problem with the radio that recognizes the fob then that would not have worked either.