There might in fact be nothing wrong with the circuit. As GoldDigger notes, LEDs will glow with very low current. Nothing is a perfect insulator, and switches have ratings for allowed leakage current; that leakage current might be enough to light the LEDs. If you have a perfectly wired 'switch loop', the capacitive coupling from black to white wire might give you a couple of _micro_ amps of current, which might cause a dim light.
I have 4 foot led utility fixtures from Costco. Perfectly reasonably quality and function...and in the 'off' position they glow ever so slightly when plugged in.
-Jon