They all have flat curves in the lows and low mids. In the upper mids, and highs, they all have a resonance - usually a peak, though it can be very damped and not stick up much, if at all, in some cases.
There are two primary things at play that affect the perception of things:
1) Psychoacoustics. If you have a big whopping peak in they upper mids, you will end up turning down the volume, and the perception is less lows or low mids - it's just a distraction thing. If you're hearing a "scooped pickup", it's most likely this at work.
If there are two pickups, and you're hearing a scoop, or you're playing through an amp (especially a Fender), it's very likely the scoop you're hearing has nothing to do with the pickup - there are very real "scoops" out there that have to do with mixing pickups and tone stacks in amps..
2) Non - linearities. This is more subtle, but it is real. When you have a magnetic pickup on one side of a string, and the string movement is a significant fraction of the nominal distance, the waveform you get out is not strictly speaking a reflection of the string's movement - it is distorted. Let's say the string is an eight of an inch away, and the string is moving half of that. At its closest, the string is now 1/2 the distance it is at rest (a factor of 2), and at its furthers, it is 1 1/2 times further - a factor of 1.5, not 2. Given that, the waveform will be squashed more on one side than the other. It's assymetrical distortion, and will give you some added stuff - primarily second harmonic of what is there. There are almost always harmonic on the string, so it will give you a bit of second harmonic of those harmonics in addition to the second harmonic of the fundamental, etc. - it creates some additional lower mid stuff. This is, in most cases, pretty subtle, but it is real. If you back off the pickup (lower it away from the strings), it reduces this effect.