https://learn.adafruit.com/adafruit-huz ... /downloads
To my opinion, this is badly designed, since the LED won't act as a PullUp until it start conducting, and even then, the drop voltage across this LED will prevent having a "good" HIGH level on GPIO0.
Therefore, you should try to add yourself a PullUp resistor in parallel to the whole LED circuit and provide us your experiments results again.
EDIT : what is also strange, is that bad behaviour about improper boot mode, should always occur, not only in OTA context.