ESP32 Forum

According to this page I could inject only 3.3V into the PICO-KIT board to run it. The schematics show no extra components, just the LDO with standard wiring.

According to web sources it is not safe to backfeed an LDO with no input voltage.

Which is correct?

It's not always safe as the 3.3V also appears on the other side of the LDO, and that can backfeed anything connected to it. For example, take a hypothetical board similar to a Pico-Kit which has its USB connector directly hooked up to the LDO. In this case, you could have a situation where you have the USB port plugged into a powered-off computer and the board being powered by an external 3.3V power supply; in that case the 3.3V power supply would try to power (through the LDO) the PC as well, which is not good.

Note that I said 'hypothetical board similar to the Pico-Kit', because the actual Pico-Kit has a diode (D2 in the schematic) to stop that from happening, making it perfectly safe to power the board from external 3.3V.

You also have to be careful with sequencing the power. I've had a 3.3V display powered from its own regulator and connected same regulator to 3.3V of the LDO. You have to always disconnect your USB before powering down your 3.3V device, else that 1117 LDO tries to power everything which it isn't happy about. It also means the ESP32 is still "signalling" an unpowered device, which can destroy it.

I've actually removed the LDO when concerned about that.

Well, to be fair, if something (like your display) has its own regulator, you shouldn't connect the 3.3V lines together anyway. Even if both LDOs are powered, slight differences in reference voltages will lead to one LDO taking on the brunt of the work while the other LDO idles.