I checked SR4a, and the entry is nowhere near similar...
Maybe it is a copy pasta error from Long Burst or Semi-Automatic burst (that both obviously allow you to take the multiple attack action on one burst). Maybe they are talking about that you are allowed to take the multiple attack free action to attack multiple targets in one burst when you dual wield. Maybe they do mean that you are supposed to split a 3 bullet burst on multiple targets but forgot to supply rules how to resolve it under the simple actions on p.165
The book is ambiguous enough to support a reading where you can split a 3 bullet burst from a burst fire weapon, but there are no rules how to resolve it. It does not matter if you or me are correct on this matter, the book simply is need of errata on this no matter how you read it.
In the meantime I choose to read it the way it make most sense (and to me it is that you can take the complex action "Fire Semi-Auto, Single-Shot, Burst Fire or Full-Auto" on p.165 or the "Suppressive Fire" on p.179 if you want to attack more than one target with a ranged weapon - without dual wielding)
There are simply no other actions that explain how you attack multiple targets with a ranged weapon (except if you dual wield).
I personally think that this is because no other ranged attacks are supposed to be split on multiple targets (unless you dual wield).
As for the scenario, as a GM I would allow this with a Smart weapon.
There are no rule support that it would be allowed with a smart weapon.
Of course you can make up all kinds of rules to make it work (i already said that).
But if you want official written rules for it then you have to wait for the errata (but there is also a chance that the errata will clarify that you can't split a 3 bullet burst on multiple targets and if you want to attack multiple targets with a simple burst fire action you have to dual wield).
The character declares his intent to fire at all 3 targets, the computer system holds firing till the weapon is pointing at each target in turn.
I can't find any reference to that either, so that would be another house rule...
...and in theory, you could split this 6 burst complex into two 3rnd simple actions. In SR5, this would be a 6 rnd burst, split between 2 targets, dice pool gets split in two, bullets get split in two, modifiers are figured out the same way. Defense penalties are figured the same way
It is not a 6 bullet full auto burst where you aim in the general direction of one target and hold the trigger for about half a second before you let go and stabilize the weapon for the remaining of the combat turn. This is a Long burst where you tap the trigger once. The weapon will automatically spit out 3 bullets. You aim at the next target and then tap the trigger again. The weapon automatically spit out 3 more bullets.
Again.. Real life, and even FPS games don't accurately convey the concepts of Wired Reflexes or Smartweapons.
SR5 combat is based on a similar Hollywood Reality you see in action movies.
It let you make amazing stuff, but there are limits to what you can and cannot do even in SR5.
I am not talking about wired reflexes or smartweapons
Benefits of using Wired reflexes and smartweapons are well explained in other parts of the book.
(having said that, rules as written for "Fire Semi-Auto, Single-Shot, Burst Fire or Full-Auto" on p.165 work very well with both wired reflexes and smartweapons).
Aiming at one target. Tap the trigger. Automatically fire 3 bullets at the target. Aim at a second target. Tap the trigger. Automatically fire 3 bullets at the target.... This make sense.
Aiming at one target. Tap the trigger. Spin around and point at different targets while the weapon automatically fire 3 bullets in a very short time-frame... And having the same dice pool to hit as the option above where you aim at two targets and tap the trigger twice...? This does not make sense. Honestly can't see how you can defend it.
Then again, in Call of Duty, there are several Breach scenes that sort of convey Wired Reflexes, and the game slows down so much that you can hold the trigger and sweep a continuous burst so that each target gets 1 bullet if you have the controller response/speed set high enough.
Even in slow motion you can't really use a burst mode weapon to tap the trigger once which will make the weapon automatically fire 3 bullets - and then land them on 3 different targets by moving your weapon around while the bullets automatically leave the weapon.
But in slow-motion you can hit each individual target with an individual 3 bullet burst quite easy...
Even if the targets are not even next to each other (or even in front of you)