SR4A pg 320: "Panther XXL: This enormous assault cannon fires special ammunition common to the primary weapon in many small tanks. It comes with a smartgun system." Stats listed on pg 321 under "Assault Cannon."
That is not, however, a "light auto cannon", which is specifically what Doubletap's player was asking for.
Gotcha, I see where I failed to make the distinction. In light of this, I would say no then, since the GE Vigilant light autocannon is a vehicle weapon which "are not intended for use by even the strongest metahuman, either because of their size, bulky support equipment, or massive recoil." (AR 123). A GE Vindicator Minigun (AR 29) would give the character the same look, style, as the Vigilant or an Assault Cannon for better punch (10P vs the 8P on the Vigilant) but at reduced (SS) rate of fire.
But if the player said they wanted to use a Vigilant mounted on a reinforced troll-sized granny-walker and wheel it around with them...sure; but the walker costs extra at Geriatrics-r-Us.

(or any other specialized modification + cost to allow for the vehicle weapon to used hand-held or semi-hand-held. And Ryo's suggestions make for a great basis on that ruling).
In Shadowrun, though, all HMGs do 7P DV -3 AP, while the Barrett rifle does 9P DV -4 AP. Meeting in the middle with 8P DV -4 AP seems fair to me.
Based on the damage values and AP alone, I would agree with you, but it's the additional stat that HMGs can fire at FA, the Barret only at SA, and the autocannon fires at FA+ (or FA-Minigun) rates that makes me think the 8P, -4 AP, FA+ isn't exactly in the middle; given that having the option to lay down 30 rounds per phase from a 200 round belt at a modified 12P, -4 AP is, well, a very handy option to have.
Though with some thoughtful modifications/gyroscope hip mount/etc, I wouldn't have too much of a problem letting a player have something like this but just so they know, once the enemy is aware of the autocannon armed troll they'll probably feel the the fastest and most efficient way to deal with the target is with a medium range missile or two from aerial combat drones or snipers or bring in the spirits or all three. Only the most idiotic BTL-slotting gangers are going to do a frontal assault on the troll. Everyone else is going to do their best not to call attention to themselves and wait to target a kill shot on the troll before engaging anyone else on the troll's team (save maybe the team's mage riding Master-Blaster style on the back of the autocannon armed troll, of course).