gather evidence in order to get convictions
That bears repeating.
The way our criminal justice system works is that law enforcement gathers evidence and builds a theory of how that evidence could prove how a crime was committed. The theory will say that one or more people committed the crime. The justice system (in abstract) presents that theory, along with corroborating evidence, to a judge (and sometimes jury).
The more evidence the justice system (from LEO to prosecutor) has to choose from, the more likely they will be able to assemble evidence in such a way that it looks like a crime was committed. That appearance, when it is presented well, leads to convictions.
Note that no crime is necessary, only evidence and a theory. Now, I'm not trying to argue that most convictions are wrongful. The people who have researched the subject say the wrongful conviction rate is somewhere between 1% and 3%. That means between 97% and 99% of convictions are valid.
The numbers are that high for several reasons. The obvious reason is that ~32% of people charged with a crime in the USA are found innocent. The more important reason is that criminal investigations are normally triggered by victim reports of a crime (or some clear evidence such as a dead body). The investigative catalyst affects the shape of the investigation, limiting theories to those involving the crime reported. Investigators are unlikely to build a theory that the evidence they've collected proves you are part of a Mexican arms trafficking operation if they are trying to prove that you are a bank robber.
However, in this case, there was no crime. The BATFE agents were not knocking on the doors of someone suspected of committing a crime they knew had occurred. They were knocking on the doors of someone that, by all evidence, is a law abiding citizen. The person they were questioning had passed a background check just a few days earlier in fact.
When investigators investigate without a crime they are freed from the requirement that their theory prove something that actually happened. That is vastly liberating. Given enough facts a competent investigator can put together a plausible theory that a crime was committed. No promises about what crime but they can put together a convincing pattern of facts to prove something happened.
That's why anyone who argues they have "nothing to hide" is simply displaying ignorance of how our criminal justice system works.
ETA: I am not saying, by the way, that those investigators are working in bad faith. They may honestly believe that the crimes they theorize happened were in fact committed. They may honestly believe that they are making the world a better place. Misguided isn't the same as evil -- that's why it's often more dangerous.