I believe he was discussing a generic magic-damage spell, not Smite. Hard to tell, though, that part is not very clear. In any case, I can understand the scenario he's talking about.
Let's create this hypothetical situation (with simple numbers to make it easy):
Kassadin (1000 health) is being attacked by two enemy champions, A and B.
Champion A is the main damage threat, capable of delivering 1200 magic damage total.
Champion B knows this, and is only planning to cast a 200 magic damage spell for the assist.
Kassadin fires his Q at Champion A in order to gain his magic damage shield of 300.
Champion B damages the shield with their single spell.
Champion A obliterates the last 100 health of the shield, and ALL of Kassadin's 1000 health.
So, does Champion B get an assist or not? He failed to do any actual damage to Kassadin, but his spell is the only reason (okay not really, but this is hypothetical) Champion A was able to finish him off.
I'm unsure of the answer to that, but it sure seems to me like Champion B would deserve an assist for his efforts.