I have found in my effort to replace nearly all of our incandescents with LED's that it takes very little power to make them glow. One thing I discovered in our home is it can matter how the light gets its power. I had 3 different areas where I had problems with glowing. When I opened the switch boxes I found that the switch had been wired into the neutral side of the circuit. So, even though there was no completed circuit there was still enough leakage to make the lamps glow. Rewiring the switches into the hot side solved the problem. In another instance I noted that having a switch with a light in it (glows at night so you can find it) also allowed some current to pass through and fire up the LED's. Finally, sometimes you come across a situation where the power is run first to the fixture and the switch is placed 'downstream' completing the circuit after the fixture. I have no idea if that is up to code and prefer not to do any of my wiring this way, but this can also cause LED's to glow.
Obviously this is not your issue because the opener is not switched. However, the unit is hot all of the time. My guess (and it is only a guess) is that the opener was never intended to use LED's and the design may allow for some small amount of current to reach the socket - enough to fire up an LED or two. This should be easy to determine using a meter. I don't see a need to replace the opener. If the 'night light' bothers you you can always go back to the incandescents. Otherwise just enjoy the 'new' capability!
“We all die. The goal isn't to live forever; the goal is to create something that will.” - Chuck Palahniuk