Frankly, I think the rules are quite clear, when read in context and not only the power focus section. Each focus provides a bonus to a specific
area of magic with the exception of power foci. All other foci either add their force to a specific skill test (Alchemy, Disenchanting, Spellcasting etc.), allow you to treat a rule differently (sustaining focus, masking focus etc.). The power focus however does not feed of a specific area of magic, but of magic itself.
Every magic test with the exception of drain consists of Magic + Something. Normal focus boost the something side while power foci boost the magic side. The semantic difference is that normal foci provide a boost to whatever you use to work magic, while power foci provide a bonus because you are using magic.
Further evidence that there is indeed no such thing as a bonus to the magic attribute through power foci:
You can’t bond more foci than your Magic attribute, and the maximum Force of all your bonded foci can’t exceed your Magic x 5. Regardless of the number of bonded foci you have, only one focus may add its Force to a dice pool for any given test.
P. 318 Core)
The above quote flat out states that all foci add their force as dice pool modifiers to tests.
When you roll dice in Shadowrun, you are generally making one form of test or another. (P. 46 Core)
A test occurs when dice are rolled. If you don't roll dice, it's not a test. Its a mathematical formula that compares values.
If the spirit’s Force is greater than your Magic rating, the Drain is Physical; otherwise it’s Stun. (P. 300 Core)
There is no mention of a test. Its a simple inequality/ equality that determines whether the drain is physical or stun.
Historically speaking. Power foci increasing magic in previous editions had nothing to do with summoning, as it was your Charisma that determined the type of drain. (Edition 1 to 3) If there was indeed an old school thought at work when it comes to summoning, it was certainly not to introduce a feature of power foci that has never existed in previous editions.
As a side note, if a power focus increased your magic rating, it would allow you to bond more foci. Sounds unlikely doesn't it?