Why do SDR receivers emit I/Q samples?
The SDR (or any general digital signal processing system) takes the received RF signal, and downconverts it from the carrier frequency to the baseband.

Now, the real bandpass signal from the antenna does not necessarily have a symmetric spectrum around the carrier frequency, but it can be arbitrary. If the downconverter now shifts the spectrum to the center frequency, the corresponding time-domain signal becomes complex. So, the I and Q samples you get from the SDR are the real and imaginary part of the complex baseband signal, that corresponds to your real passband signal around the carrier frequency. 

More details can e.g. be found at the wikipedia site for digital down conversion.  

To answer your question:

I/Q representation does not correspond to different sampling points of the signal. Instead, it corresponds to the real and imaginary part of the digital complex-valued baseband signal. These parts are obtained by separately multiplying the RF signal with a sine and a cosine and sampling both streams after low-pass filtering. 

Sampling with double frequency can yield the same information as I/Q. It would be neccessary to homodyne the signal to $f_s/4$ to get all information that would have been in the baseband IQ signal to be in the passband signal at $f_s/4$ (where $f_s$ is the sampling rate).