No, it isn't flawed. Your camera wants to expose everything to the same level, medium gray (18%) regardless of how bright or dark the scene is. It will try to make bright scenes darker to get to medium gray and it will try to make dark scenes brighter to get to medium gray. When it does that, your histogram will look centered - but all scenes are not medium gray and we don't want to expose them that way, as you have discovered. That's where exposure compensation comes in and it is subject to personal taste. For example, it's a rule of thumb that snow scenes need to have a stop or two of positive compensation added to make them look proper, otherwise, you end up with a flat, gray (medium gray) scene instead of a natural bright, white scene.

By spot metering on a white area, you are telling the camera to expose the white area to medium gray. That may be the correct exposure or it may still make the scene a little dimmer than you'd like since the white area may have been brighter than medium gray, so the camera will under-expose it a little to get it to medium gray. Because the overall scene is exposed to be darker than medium gray, the histogram is shifted to the left - but that is ok because that is close to what you wanted anyway.

If you shoot in raw, you can further adjust exposure in post processing so the scene looks exactly like you remembered.

I took the following shot to post on my facebook page. I used my D7000 AND flash. I cranked in negative EV on both the camera and the flash to get the scene to look as dark as it really was.

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Attachment #1, (jpg file)