This is unfortunately a big arguing point, so I am just going to state the points and you will have to get a GM call.
1. Gunnery is a matrix action while jumped
2. Hot-sim provides +2 to matrix actions pool while jumped in
3. The description of the Rig says it provides +1 to matrix actions while in hot-sim
So the arguments are:
A.The hardware hot-sim bonus is a more specific rule for then normal hot-sim bonus. (you only get +1hotsim)
B.The hardware hot-sim bonus and the standard bonus are separate bonuses and stack. (you get +3 hotsim)
C. The hardware bonus is a typo, because the book is badly edited and organized. Same matrix, same bonus (+2)
There is no errata or "official" clarification. Some of the moderators on the forum have stated it is B. That however is not official. Most people say A makes hot-sim pointless and B makes hot-sim riggers better then hot-sim deckers. So we wait for Rigger5.0 errata and hope they clarify. That is the most honest clear answer I can provide.
My opinion if you care is B, but I play a rigger and decker or GM might disagree.
You have an error in your (3) and it is three-fold.
3a) Description of Control Rig gives the bonus as
its rating3b) Bonus is to all
vehicle skill tests, not matrix actions (although vehicle tests are matrix actions while jumped in)
3c) Bonus is while
jumped in, not while hot-sim (but you can be hot-sim while jumped in)
So it really works out like this:
1) Vehicle tests are Matrix actions while Jumped in
2) Hot-sim gives +2 bonus on Matrix actions
3) Control rig gives +1 per rating while jumped in.
Since 2 and 3 are not mutually inclusive or exclusive the bonuses cannot be assumed (in any way) to be the same bonus. You can perform vehicle actions through the matrix while not jumped in (Remote Control), and if you are hot-sim you get a +2. Likewise, you can use a Control Rig and jump into a vehicle and get the bonus from the control rig on all vehicle tests, and if you are hot-sim you get an extra +2. The text in the two separate sections don't really overlap the way you make it sound like they would. They don't have similar phrasing and as I pointed out, they don't even apply in the same circumstances.
There are quite a few bonuses for using a control rig (See page 452), but in exchange, you take damage to the vehicle as biofeedback. Likewise, there are a few bonuses for using hot-sim (See page 230), but in exchange you take bio-feedback as Physical damage instead of Stun.
| Remote Control | Jumped In |
Cold-Sim | No bonus | +1 per Rating |
Hot-Sim | +2 dice | Both bonuses |