Hulu Plus is a tad confounding at the moment. Basically you pay $10/month for the right to watch Hulu on things that are not PCs. And if you can use a PC, you can get Hulu for free. Yes, Plus has more content, but the vast majority of Plus users aren't paying $10 for the extra stuff, they are paying for the ability to use it without a PC (iPad, PS3, whatever).
Now, Plus is immature and Hulu might find new ways to drive the PC crowd to Plus. 1) They could go license more content, even bad content, like Netflix. 2) They could reduce what's on the free version. 3) They could make Plus cheaper. It's hard to reconcile the pricing of Netflix and Hulu Plus right now. Netflix may have less recent TV (well, it does and it's almost infinitely less recent TV) but it has much more older films, a lot of older TV, and the content library seems to grow weekly. Oh, and Netflix sends you up to ~5 DVDs a month for that price too (including the back and forth travel time). Finally, it's cheaper than Hulu Plus.
The reason why Hulu hates the Boxee Box-type solutions is that otherwise, those people might pay $10. They hate PlayOn too (so do I, and I bought it) because it does the same. PlayOn is effectively impossible to stop so long as free Hulu runs on web browsers. It's such a kludge that no one really cares.
If the Boxee Box is as niche-y as I expect, it should run Hulu without too much grief. If the Boxee goes mainstream -- which I doubt -- they will probably intentionally stop supporting Hulu regular and make the deal to run Plus. In fact, they are probably negotiating right now with Hulu and reminding Hulu, "Well, our buyers want the free one and you really can't stop us since we can look exactly like a PC, good luck detecting that, yada yada." How this turns out, I don't know.
For me, regular Hulu does the job and so I hack it with PlayOn. Come early next year, I'll probably buy a Zacate-based HTPC since I see that as much more future proof than one can buy in a quiet, low-power system right now. But I have a Boxee on pre-order and am cautiously optimistic it will do everything I want/need -- for Hulu and otherwise.