I am wondering if this is true or not.

Of course it's not true. Discovery and The History Channel give a lot of airtime to crackpots like Giorgio Tsoukalos, aka "the Aliens guy" and others because it gets them the ratings they want, not because they're necessarily interested in discussing factual events. The Latin word for copper itself, cuprum, is derived from the name of the Mediterranean island of Cyprus because that's where the Romans mostly got theirs from. They still produce copper to this day.

Also, if they new about the New World before Columbus, why didn't they colonize it ahead of time?

Copper is all around the Earth. You would have to have all of Eurasia and Africa ignoring their own copper deposits and somehow developing a trade route with pre-Columbus America massive enough to import all their copper needs but also forgettable enough to not be attested in history anywhere.

Sounds like you saw the "Great Lakes Copper Heist" episode of America Unearthed, a program on the History Channel that favors a lot of outlandish fringe theories about American archaeology. If it wasn't that program specifically, then it was certainly one drawing on similar ideas about an ancient New World-Old World copper trade.

As this map shows, there are many copper producing sites in Europe, particularly in around the Carpathians and the Caucasus Mountains. So its not a lack of copper in the Old World that this particular fringe theory is built on.

In this post, I went over the 'evidence' that the proponents of this idea have put forward. In particularly, "Great Lakes Copper Heist" focuses on the 'missing copper' angle which is the last point I discussed there. The short of it is that the whole "missing copper" angle is based on old, faulty estimates about how much copper was actually mined in the region that inflated the numbers to over a billion tons.

The people largely responsible for establishing the copper industry in the western Great Lakes are known, archaeologically, as the Old Copper Complex - a series of related cultures that began using copper 6000 years ago. About 3000 years ago, as their trade routes began to extend over much of eastern North America, the Old Copper Complex evolved into a new series of cultures that place greater restrictions on the usage of copper, replacing most of their copper tools and weapons with stone and expanding their ornamental and ceremonial applications of copper. Since the use of copper tools and weapons are one of the defining features of the Old Copper Complex, as their society changed in the wake of these new trading systems, they stopped being the "Old Copper Complex" but you shouldn't think that they mysteriously vanished.

In this post /u/pfaf and I discuss the 'end' of the Old Copper Complex in a bit more detail. In this post, I discuss the mining techniques employed in the region.