I'm not a big fan of Chemi-pure elite. It's mostly carbon and GFO. While it does work, it's expensive and the carbon and for best results GFO should not be mixed together. Ideally, you should run GFO in a reactor such as a phosban reactor, This it to prevent the media from clumping. As a note phosban is GFO. I much prefer to run the two media separately.
On GFO itself. I found it best to get this from a place like bulk reef supply. You'll notice that they sell several grades of the product. This is a case where you want the higer grades, because it's less bulk to ship and you'll use less product.
On carbon. Carbon is a bit controversial as a media. Some use it all the time, some use it once and awhile, others not at all. There is no right or wrong way here. This is also a media that works best in it's own reactor, but putting a bag of it in the tank will work ok.
On Polly filter pads. There are several other similar media out there. Purigen is one. In my opinion they all work. The nice thing about polly filter pads is that all you got to do is drop them in the tank. Another advantage is that they will turn different colors depending on what they are removing. They are good at removing heavy metals. The downside is that they are fairly expensive. This is something that may do you a lot of good, and sure isn't going to hurt anything.
As for "just let my tank balance out itself. Just leave it alone", this would be good advice if you were not having a problem. Often the best thing you can do on a reef system is leave it alone. When you have a problem though, you need to work on it, go carefully, and so on. If you don't work on the problem, it's very simple, your not going to solve it. Personally, I think you got quoted one of the guys "stock lines" which is not applicable in your case.
Lastly, don't put too much credibility in anything related to the show Tanked. Most of these systems are done so that the aquarium maintenance company can keep them going. As such they need to set up simple tanks, with limited livestock. In SW systems they do, the systems tend to be FO or FOWLR and those are not nearly demanding as a reef. I'd love to see a follow up show and see how all these systems looked 6 months and 1 year later.