The Shadowrun rules often call for a plus or minus dice modifier to a test. These modifiers can result from injuries and situational factors that affect what a character is trying to do.
Note the section header, Dice Pool Modifiers. This section defines dice pool modifiers and gives you two choices:
(a) Injury dice pool modifiers
(b) Situational dice pool modifiers.
The way that's worded, this isn't necessarily an exhaustive list. However, the rest of your analysis is pretty solid.
The impression I've gotten from developer comments (in the FAQ and on Dumpshock) is that the rule is intended to allow realistic situational modifiers while denying cheese. Unfortunately, there's no bright line between reasonable and cheese. The FAQ says to watch for the key phrase "dice pool modifier," but that leads to treating spell foci and weapon foci differently. Why? Is multicasting more cheesy than multiattacking?
As for specializations, I could see why people would interpret those as being "skill" dice rather than dice pool modifiers. On the other hand, they
are situational modifiers ("when the particular specialty applies"), so it also makes some good sense to treat them as dice pool modifiers.
Oh, also:
Unless otherwise stated, any modifier mentioned is considered to be a dice pool modifier.
The "otherwise stated" modifiers are things like the skill modifiers granted by the Improved Ability power. Those are subject to the modified skill maximum (1.5 × the natural skill rating) and do count as part of the base dice pool. Attribute modifiers (augmentations) are another example. I don't know if there's anything else.