You're not the first to propose this. While it does essentially solve the dilemma of her existence, it has some problems.
But Namine demonstrates a range of characteristics - such as intelligence, memory and emotion - that all other Lingering Sentiments thus far lack, not to mention her birth was different to the creation of all understood Lingering Sentiments.
We haven't exactly been able to gauge the Linger Spirits' intelligence, but I think it's safe to say that they are sentient and self aware.
The same goes for memory. We don't know exactly what the natural state of memories is for a Lingering Spirit. However, based on LS's dialogue with Sora, it appears that they retain some memories, but not completely (hence the confusion).
We can't really compare the state of memories to Namine either simply because, like with the LS, we don't know the state Namine's memories were in. DiZ mentions that she lost her memories like Roxas, but to what degree, we can't say for sure. Either way, she was able to know who Sora, Kairi, and Riku were.
As for emotion, I think it's undeniable that both Namine and the LS have the capacity to feel.
Instead of trying to compare the mental and emotional aspects of Namine and LS (since we know so little of either), you should be looking at what's right in front of us- the physical. Namine, through whatever means, has a body. The Lingering Spirits, while not entirely confirmed, seem to only possess material left behind by the original being (ie armor). When we read about the LS in Nomura's interviews, he refers to it as the remaining thoughts of Terra animating his armor, with the emphasis being on the armor. It's not as if Nomura says that it's an entity which fills the armor, but something that possesses the armor.
And then you bring up a good point about her birth. Namine was born in a different realm, like a Nobody should, but from what we've gathered, Lingering Spirits appear in the same location that their originals perished.