Not true anymore. I have an LED "over 80 inch" center marker light I just put on my boat trailer that works either way. And since it is sealed, I can't look to see if it is perhaps a double LED configuration.
You are correct however here is the long explanation. I apologize if it is long winded. I wanted to do a simple explanation for those that are frustrated by all the different answers you get in led threads. If anyone sees any errors feel free to correct them. I am in a long line up and keying this in through the quick reply on my phone while i am waiting so i can only see a couple lines at a time.
A single led is always one way only because it is a diode and that is how they work. It is possible to build an array(this is what we usually replace our incandescent bulbs with) of leds that is non directional but this requires additional electronic components that the cheaper manufacturers eliminate.
That is why reversing them is always the first thing to try. If he had power with the bulb he was replacing he's should still have power with the led. Another possibility is as others have mentioned a bad ground.
Other likely culprits are a bad fit between the replacement led and the socket or low voltage. LEDs are much more limited in the range of voltages they will work at. While an incandescent will just be dim at a low voltage a led will not turn at all if it is below a certain threshold. Again there are things they can build into the electronics to extend the upper and lower voltage range but that increases the price so you don't see them in the cheaper ones. The cheaper ones tend to use a resister to try to protect the led from excess voltage and that extra voltage gets turned into heat. That is one of the reasons some people have ones that get very hot and others don't
This is why we see do many different answers to questions about LEDs. Everyone is right because it depends on the other electronics in LED arrays they bought.