You're reading the letter of the law correctly. By the letter of the law, yes you can be arrested for being armed and then have to present your HCP to the judge to get out of it.
In "reality" that's not going to happen for a whole host of reasons, not least of which is that no cop wants to have to explain to his captain or the judge why he's wasting everyone's time for no reason.
As I understand it, the nuance of TN making an HCP a "defense" to an unlawful act is that it opens up options for Law Enforcement to do things legally such as confiscate the weapon during a stop. You're breaking the law by having the loaded gun, so they can take it from you while they check out your "defense" in the form of an HCP. Basically, they get to treat you like a criminal until they have solid proof that you aren't, because by the letter of the law, you are a criminal by being armed.
If the law against being armed was worded to be null and void for HCP holders rather than just a defense to that law, then law enforcement probably couldn't legally do that since you wouldn't actually be breaking any laws. They could still stop you and ask for your permit if they saw the gun, but could not take it during the stop.
Again, that's just as I understand it, but the reality is that with an HCP you're good to go as long as you're not in a prohibited place.
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monkeylizard's post in Can someone please explain “with the intent to go armed� to me? was marked as the answer