I would allow the Reflex save for an unconscious character.
Should a character with Lightning Reflexes use the +2 when unconscious? Should an unconscious Rogue be better than an unconscious Wizard at saving from a Fireball? Probably not.
On the other hand, what about a character with an item that grants a luck bonus to saving throws, should LUCK be negated when you're sleeping? Cover gives a bonus to Reflex saves because it increases your chances not to get caught in the blast, even if you're bound in chains behind that cover; if the Monk here had almost-but-not-quite-total cover, would he still have no save?
All in all, it seems to me that different rationales play part in the concept of a Reflex save, and I bet that different authors/designers/sages/customerservices have ruled very different things in time because each of them has its different idea of what a reflex save should be.
(It's a similar thing as the occasional contraddictions with flanking: half the designers conceive flanking a vision problem, the other half conceive it as a position problem.)
For that reason I really don't want to read too much into a sentence which, when talking about a specific thing (Evasion), it infers a general rule which isn't mentioned in other places... I just don't know what had the writer in mind when he wrote that.
And about objects, why don't they get saving throws? I think the reason is simply that designers thought: "who cares about objects?" until someone pointed out "well, I care about a magic sword...", "you're right, magic objects should get saving throws, let's explain it because they're magic".
What I mean to say here is that I would never think my DM is "wrong" if he allowed no ST in this case, I'd just be fine with it. But when I am the DM instead, I don't either consider myself "wrong" because I allow it. I can see common sense in both ways. Probably there's slightly less sense in my choice, but I have other reasons to do so.