Your response sounds very theoretical. To be honest, in many companies the reply will be very easy: go.
Well, given that it was a discussion between instructor and student, and I've been an instructor and check pilot, yeah. I suppose it does come off that way. But I always look at these situations as though we're training Captains and future Captains on how to think problems through. I never talked about subsequent failures, just that the warning light can illuminate for different things other than, in this case, a bleed leak. While the MEL may not apply for the light in one case, it may in another and we don't know that until we talk to maintenance. When reading the first post, it struck me that the OP may not yet have had the experience where a straightforward situation is not straightforward at all, hence I suppose I did put more theory into my response.
With that said, it's certainly not my experience that maintenance will just say go. Maybe I've been lucky, but at the four airlines I've worked for, it was the opposite of what you're suggesting. I'd think we would be OK, but they'd apply the MEL anyway (assuming it applies). Hence, if they say go, go. If they say don't go, don't go. I'm not naive enough to think this is how it is all around the world, but we can only ever answer based on our experiences, no?
Also, while a dispatcher may not know about the aircraft systems, they nevertheless have co-authority over the flight until takeoff. That co-authority means that I call the dispatcher first to tell them we've had a problem and that I need to talk to maintenance. In my outfit, this ends up being a conference call between me, the engineer, and the dispatcher. I tell the engineer what happened, they tell me whether or not to apply the MEL and, if needed, the dispatcher begins working on a new OFP. It ends up being far more collaborative than other spots may be and often avoids the need for me to say "I'm AOG, deal with it" - although, I do keep that in my back pocket if I feel I need it.