It's been previously established that if you begin to cast a spell whose cost you are able to produce enough mana to pay for, you must do so:
[...] you are committed to completely cast a spell you've decided to cast. (source)
No, you cannot choose to stop casting a spell once you have announced that you want to cast it. (source)
In contrast, the assist keyword ability has had this said about it:
If they don't want to pay, you can either foot the entire bill yourself, or choose to back up and not cast the spell at all. (source)
This appears to rely on the player's ability to back out from casting a spell even though they would have been able to cover its cost. Nothing in the rules for assist seems to grant the player this ability, so where does it come from?
Follow up question: When casting an assist spell, are you able to back out only if the other player paid exactly zero mana, or can you also back out if they didn't pay as much as you would have liked (even if you could have paid the rest of the cost)?