I think the real question here is .. if your wizard knows the radius of the fireball spell, and was able to look into the room to get a general idea of how big the room is (volume-wise as compared to the volume of a fireball spell), and knew the paralyzed barbarian was in the room... why did the wizard cast the fireball spell? Seems like a jerk move.
I think from that alone...
if wizard didn't know the barbarian was in the room, and/or didn't know they were paralyzed, then wizard shouldn't be able to sculpt spell to try to avoid them.
if wizard knew the barbarian was in the room and the barbarian was paralyzed (and knew the barbarian's location), then I would think just some simple role-playing could take care of this whole problem:
(gm) "Barbarian is paralyzed on the floor in the corner."
(player) "Ok, if I cast a fireball in the room, could I place it in such a way that something like a big table or something would protect him from the blast?"
(gm) "Um.. sure."
(player) "ok.. fire in the hole!"
(gm) "BOOM... the fireball goes off in the other corner of the room, creating a blast pattern that engulfs the enemies. Any blast that would have hit the barbarian is absorbed by a flipped-over table."
Basically, what I'm saying is... as a former GM.. I would prefer to role-play a solution instead of rules-lawyering it.
Often we get questions on here about situations AFTER they happened in someone's session, and a player is trying to post-mortem rules-lawyer the situation to rub their GM's nose in it.
Even though you found rules to support your argument, I would say it's a moot point if the situation already happened and the GM already made a ruling during play, even if it was a ruling you didn't like.
The whole point of role-playing is to abstract reality in order to provide more ways to interpret situations with role-playing. WotC have gone a bit over-board with creating more and more rules for every situation under the sun, and thus it's gotten more and more players lately turning into rules-lawyers and tactical micro-managers. If that's what you group and GM like, then go for it. But, you can find tons of cases like this (two conflicting rules) in the rules lately, and all it does is cause confusion and debate.
That's why I always focused on RP solutions first, and rule solutions second.
May not be the answer you want, but it's just I'm noticing a LOT of very detailed, minutiae-related questions on the stack exchange RPG posts lately, trying to dissect rules and find some way to min/max something or justify something. All of which seem like things that RPing could solve if folks would RP it first instead of rules-ing it first.