I'm not a doctor, but I can say this. Morning wood is a real thing, and so is having to piss. You generally are forced to angle your whole body in some sort of toilet yoga position in order to pee, but it obiously has to be done.

I think the word being misquoted might be "arroused". I've never actually tried, but I think it may be impossible to masturbate and piss at the same time. An erection in and of itself doesn't necessarily mean you are sexually aroused.

This might turn into one of those " do women really have orgasms" as all men might have different definitions and concepts behind what constitutes an erection. I do indeed have trouble pissing after any kind of sexual contact. It usual takes a bit for my body to adjust and calm down. Whether I finished the deed or not, it's a process to prepare my body for regular functions. But morning wood isn't in that same category. I'll also add that I don't ever have to wait for an erection caused by sexual contact to go away before I piss. It just takes a bit of concentration to flip the mental/phyiscal switch back into it's other biological function.

This is all anecdotal obviously, but I can say for a fact that with the definition of an erection just being the blood flowing through genitals, it is indeed more than possible to piss. It's something many of us do on a daily basis.