We can do both.
As a player though I would be thinking "hmmm we are crap at defending free kicks, maybe I should not give away this TOTALLY UNNECESSARY foul."
Also there probably comes a point where is a professional defender who has played there all his life, you take a look at how we defend set pieces and think "maybe I should try something that does work" instead of blindly following the zonal plan.
You defend as a team. Zonal just places less emphasis on individual responsibility than man-marking (i.e if your man scores, it's your fault).
If Silva is using a zonal system and we have one man within that who goes "maybe I won't follow this plan" as you suggested, that's EXACTLY where we'd be going wrong.
Zonal isn't the problem. The system works. Lots of teams in England and across Europe use it effectively. In fact, I think i'm right in saying the two best defences in the league currently use it.
It's poor execution and implementation, but lots of teams do suffer in the immediate aftermath of switching from a man-to-man to zonal system as it can take some time to get your head around your own personal responsibility and where your invisible zone boundaries begin and end.