Something I came across whilst discussing character ideas with one of my friends, in each schools section under arcane schools, is that it doesn't state that the spell added has to be arcane, just that it has to be of the appropriate school. As a GM I am reading it as way for a wizard to add a spell normally found in another school to your spell book, which I think is an interesting idea, especially since I have noticed many complain about the shortage of many types of spells on the arcane traditions list. I would like to know other's opinions on this, of course, I would probably still run it as i read it in the future games I run.
The Arcane Schools section states "You also add another arcane spell of your chosen school to your spellbook" (page 137, top of second column). Pretty sure the individual "you add a 1st-level abjuration spell" bits under the schools are just implementations of that line, in which case they inherit the "arcane" restriction.
Also, the Arcane Spellcasting class feature says "You have the power to cast arcane spells using the Cast a Spell activity". So even if you could learn spells of another kind (which you can't), you can'couldn't cast them.
I'd agree that the intent is likely limited to arcane spells, as the section talks about arcane spells and doesn't explicitly give you an exception.
However, now that you have me thinking about it, it could be a really cool ability if Specialist Wizards could grab a couple spells off other lists that were part of their specialty school. Other casters have some kind of limited access to spells outside their school (Cleric Deity Spells, Sorcerer Bloodline Spells, etc.) so allowing Wizards a limited selection shouldn't be too powerful and would really help to differentiate specialty wizards from each other or universalists.
The arcane spell list is already the largest one by far (50% more spells than divine!). I really don't see any reason to give the wizard even more options.