Baseband Signals have zero imaginary component
You're right, but you've misread the sentence:
Baseband Data Communication means that there's no $f_c$.
For example, your USB cable to your keyboard, that's baseband communication. It can only carrier real-valued signals, so you only get to choose one dimension, not two, of signal freedom.
This is opposed to passband systems, where you can modulate the baseband signal up to a carrier frequency, which means your negative (relative to $f_c$) frequency spectrum doesn't have to have the same content as the positive.