No, you may not "accept" zero burn
Accepting burn means you must accept to take Burn to activate/use that ability. There are many abilities that reduce Burn cost, and taking those mean that your character is not "accepting" the Burn.
This has been clarified by Mark Seifter (Designer) a few times, but never made it to a FAQ, for some weird reason, as seen here (and confirmed again here):
If the Kineticist accepts burn, does that activate everthing that feeds off of it? such as the bonus to hit and damage from Feel the Burn and the damage dice from the fire skin effect? And by accepting burn that means not using things like gather power to defray it?
If you wind up with burn for any reason, you get elemental overflow (feel the burn) bonuses. However, more or less everything else in the class that asks you to accept burn is in the form of "accept burn to get benefit X from me." So if you accept burn for your fire skin, you get more fire skin (and having it also triggers elemental overflow), and if you accept burn for a giant blast you get a giant blast (and also elemental overflow). You are correct that defraying burn does not count as accepting it.
There is one exception to this, the Internal Buffer ability, as clarified by Mark Seifter again:
Many of the kineticist powers specify that it will do something extra if you "accept burn". My question is, given that as you level, there are more options to reduce /get rid of burn, would that still count? So, celerity says if you accept burn, Haste lasts 1 Rd /kineticist level. If I use my buffer to reduce the burn by 1, would the effect still take place?
Paying out of your buffer still gets you the effect you want, though it doesn't increase your elemental overflow (overflow requires you to actually have burn).
Keep in mind that there are no abilities that help you reduce the burn cost from defense or wild talents (that I know of), so the only way to reduce the burn cost of a wild talent to 0 and still benefit from the effects of Shroud of Water would be using the Internal Buffer, as the ability says:
Whenever you accept burn while using a water wild talent
If you search through the wild talents, and they all have a similar wording, and thus should work the same way.