Hi and :welcome:
It's not really the bioballs themselves that cause the problems. Basically, if you rely too much on just bacterial filtration (aka biological filtration) with no good means of denitrification you'll ultimately end-up with a nitrate surplus. If you're exporting wastes before they are broken down into nitrates and/or you have an effective means of denitrifcation you can keep nitrates in check.
There are a couple of philosphies really. Some prefer to aggressively remove nutrients BEFORE the bacteria even get a chance at them. In a reef, this is generally done via heavy skimming, water changes, frequent detritus removal (syphoning, rock "storming, etc.) activated carbon use, etc. Another popular train of thought is to soak up accumulating nutrients by growing macros in a refugium (algae filtration), encouraging lots of denitrification by using a deep sand bed, etc. Many use some combination of these techniques. Personally, I've come to favor the former method because I feel it's more reliable in the long haul and feel I have better control over the system's health, but that's JME/JMO.
It's a balance thing really. If you are exporting wastes quickly enough, nutrients won't build-up and you shouldn't have a big nitrate (or phosphate) problem. If you're not exporting wastes quickly enough you'll need some form of dentrification and/or phosphate export (for example harvesting macros) to keep the end-products (nitrates & phosphates) under control.
Of course, the amount of waste being generated to begin-with is a big part of the equation. If you stock and feed heavily you may find yourself having to employ several techniques in concert to keep things manageable. If you stock and feed lightly, you can get away with much less.
As for media like bioballs... ...if you keep the biomedia clean (generally done by using a prefilter and cleaning it regularly) they can provide very effective biological filtration, but then, so does live rock. One disadvantage with plastic biomedia, however, is that it will not provide any dentrification like live rock does. For that reason, in a system where you might otherwise have some accumulation of nitrate, the live rock can provide some denitrication to neutralize this whereas the bioballs won't.
The bottom line... ...IME if wastes are being removed aggressively enough you can have a nitrate free system with a variety of methods. That said, it's much easier to accomplish this in a system with plenty of live rock and a good skimmer, vs. trying to do it with a wet/dry filter. Also, the live rock provides a natural look as well as habit for a lot of reef critters. For these reasons, most people today recommend live rock for a reef tank.
HTH
