If they employed incandescent lamps then I'm inclined to believe they used a "coincidence" detection. (The timing of trigger & photodiode being the same.)
Small incandescent lamps can be modulated, but only by low frequencies. It is possible to add this method to the timing method for improved discrimination.
For your application with LED's I'd try to use a high modulation frequency, like 30, 35, 40, 45kHz and so on, in addition to timing coincidence.