Well first of all, "you have me" is very different from "I'm here". Furthermore, she was in the MC's arms, clearly turned on, to me, in that situation "I want you" means, "I want your mouth on mine" not "let's make babies and spend the rest of our lives together".
To be specific, she said "A special relationship of trust", which can mean a hundred different thing, including "best friends" or "friends with benefits" or "non-exclusive lovers". Saying you have "A special relationship of trust" means less then a fart if you don't elaborate. Hel, I'm in a special relationship of trust with my mother, am I supposed to be fucking her now? Exclusively?
And not answering a declaration of love is a pretty clear message of where he stands.
Lastly, she didn't say she wanted him for herself, she said "when you appeared, I started wanting everything for myself". That, just like the relationship of trust thing, can mean a hundred different thing and is far from a clear message, so saying they where not exclusive is still an incredibly good excuse, becouse the fact is, that it's true. Yrsa kind of tip toed around such things and the MC never said anything about it.