I didn't say you SHOULD do that.... just suggested there's unlikely to be a big issue if you don't happen to have it with you, but have a good copy. Certainly try to keep such a valuable document in protective cover always.
A good photocopy will usually be ok, if the photo is clear and looks like you.... if not, they may come with you to see the original.. depends on the reason they want to see it, and the mood of the officer ( like most of the world )
Once I came in on a two month tourist visa and officer stamped 30 days - probably thought I was on visa exempt. Didn't notice it til next day so had to go to immigration , well-dressed, and explain, without blaming immigration ;) . Fixed. I always check the stamp immediately now. Good luck.