I disagree. Although it's never really been the best science fiction in regard to explaining things the universe is presented in a way that everything has a scientific explanation (or at least is supposed to). There isn't any magic. There is certainly unexplained but the assumption is that everything in this universe has a basis in either real or imagined science. Therefore, Science-Fiction.
I think the only way that explanation works is if you assume that "magic" itself has a scientific explanation. There are plenty of examples where the "science" is not only wrong, there's often no explanation for how it works because we're just supposed to believe it does.
Example 1: The Sonic - What does it do? How does it work? How do Sound Waves re-attach barbed wire? Or manipulate a computer? Etc. This is part of the complaint in this thread - there's no boundaries for the Sonic, it's just a Magic Wand. In fact, The Doctor didn't even make it himself, it's something that comes from the TARDIS! We might as well say it has a Magic Feather core.
Example 2: "Timey-Whimey" - So, instead of The Doctor trying to explain how it works, he pulls out this phrase (or something like it). In a Fantasy work, when someone asks how things work they say "it just does" or "it's complicated" and move on. In a Science Fiction you take time to explain something (even if it's made up).
Example 3: "Remember Me" - So Amy brings back The Doctor (after he uses the Tardis to restart The Big Bang) just by remembering him. Don't get me wrong, I absolutely LOVED the scene - very powerful and emotionally driven.... but not Science Fiction.
I could go on, and on, and on. The writers and producers themselves have made it pretty clear that this is Storybook Fantasy. Even as far back as the "Rose" era (I can't speak to the older Who because I haven't watched much of it) it was a work of Fantasy instead of Science Fiction. Rose absorbs the Time Stream and wishes the Daleks away - Science or Fantasy? The Angels turn to stone the moment somebody looks at them... there's no way Biology works that way.
You see, in order to be a "Science Fiction" you have to maintain some sort of "plausibility" - the vast majority of stuff in Doctor Who is VERY implausible. In my mind, Doctor Who doesn't even make it into the Pulp (of SciFi) tradition of Science Fiction. There's rarely an explanation of how things work and when there is, there's very little attempt to keep it in the realm of plausibility.
In Doctor Who, we might as well be saying "A Wizard did it" - and that Wizard is The Doctor.