Passengers can and usually do board the aircraft while it is being refueled and catered.
It's not so simple.
Refueling while boarding/deboarding is allowed, but with several restrictions depending on airline, country and airport regulations (some airports ban it altogether, some requires to call a fire brigade, etc. ) that might not worth the trouble. For example, most regulation call for passengers to remain seated with seat belt fastened. Same for catering, it surely can be done, but having passengers moving through the cabin together with catering crew might be messy.
So, we just assumed our airlines do one thing at once.
