He is using ‘nature’ in the philosophical sense. IE, it is my nature to be antagonist and argumentative, but it is not one of my physical attributes. I may change my nature be attending anger management courses, but my physical self will remain unchanged.
Since such failures are a daily reality of the Christian life, I think that pushes it back down into the realm of the trivial.
How about if we all sing:
Two, four, six, eight,
time to transsubstantiate!
So get down upon your knees,
fiddle with your rosaries,
bow your head with great respect and
genuflect, genuflect, genuflect!
Oh, no, you should never be praying the rosary during the consecration! Better get it straight, or the nuns are going to come & whack you with a ruler! 
No, I get that, But the sentence I parsed seemed to not follow his logic.
Since this is a scientifically unverifiable claim, should I give it the respect and reverence I give all other scientifically unverifiable claims?
The aside about ‘breadiness’ might be confusing, but taking it out, I think it parses pretty straight forward…
“Catholics believe that the substance of the bread changes, but the accidents of the bread remain the same. The substance of the bread refers to its actual nature, a quality utterly separate from it’s physical characteristics, or accidents.”
Then how can it be a valid claim? Bricker designated it The Truth, and yet the claim is vaguely defined and utterly unsupported other than by “take our word for it”.
But nontheless these are qualities inherent in yourself that others merely observe and reflect. If you were to be described as “popular” or “wrongfully convicted” it would be a status imposed upon you from outside and not neccessarily reflective of any aspect of your character.
You’re not entirely wrong.
This seems a thread for long-winded posts from me, so I’ll give you a fer-instance. In Catholic practice, the only day of the year in which Mass is not celebrated is Good Friday. The church is draped in somber colors, and the tabernacle (the place where the consecrated host is ordinarily kept) is left standing open and empty.
Now, when an observant Catholic enters a pew before Mass, he typically genuflects – briefly kneels on one knee and blesses himself with the sign of the Cross. This is done to show reverence for the real presence of Christ in the tabernacle.
Come watch a Catholic service (not a Mass, but a service!) on Good Friday. An alarming number of Catholics enter the church, find a pew… and genuflect! This raises two questions: what are they genuflecting to? And… what have they been genuflecting to the other days of the year?
When ritual observance takes the place of understanding and knowledge, bad effects are likely. It’s even so in this case.
Someone fully aware of our doctrine should know that no harm will come to Christ if a consecrated Host is flushed down a toilet. If it’s being done, though, as a deliberate insult, I can easily see someone wishing to put a stop to it, simply because it’s a deliberate insult profaning something we hold very holy and sacred. In the same way, you might hold up a sign saying that my mother is a prostitute, and I would wish to stop you – not because the sign makes it any more likely that mom will suddenly put on fishnets and hit the docks when the sailors come in, but because it’s intended as an insult and I don’t want to be insulted.
Obviously, shooting you dead for holding up such a sign would be ridiulous – even as death threats for profaning the Host are ridiculous. But recognizing them as an insult and seeking their end is not so crazy… assuming an insult was meant.
Which came first, the Hostess or the Twinkie?
Give the heathen a kewpie doll!
Not asking you to take it seriously. Just asking you to understand that it’s not falsifiable, and so lab tests aren’t a way to show how silly it is.
You mean, like mathematical claims? 
Though there is no way to verify it scientifically, the basic essence of the wafer has changed.
In what way is this different from homeopathy?
It’s an article of faith that she remained perpetually virgin until she was assumed bodily into Heaven, yes. But as any of several of my old high-school girlfriends could aver, the presence or absence of a hymen is not the definition of virginity. We don’t know if Mary was a vigorous horseback (camelback? goatback?) rider, for instance. Virginity simply means that she never had sex; it’s silent on the issue of hymens.
I still think there is a problem. Sentence one sets forth the notion that there are two qualities: substance and accident, and that the accident is the thing that remains the same. That the substance changes.
Sentence two states that “substance” is “utterly separate” from the mere "physical characteristics, i.e., that which does not change.
If I understand the point, and I’m pretty sure I do:
Accident = physical characteristics, breadiness
Substance = whatever meta qualities it might possess. It goes from being just an object to an object that is now holy
On the material’s end, there’s none.
On the effects end, my understanding is that homoepathic practitioners claim success in treating various ailments and maladies, so a test could presumably be developed that would falsify those claims.
We don’t claim any measurable change in the bread’s physical properties, nor any measureable physical change in those that receive it.
It was just yummy bread until Hostess imbued it with “Twinkiness”.
All of this kind of reminds me of the time Rick Monday stopped those guys from burning a flag in the Wrigley Field outfield. Of course, no harm would have come to the US if he had just stood there and let them do it, but he apparently felt it was his duty to stop it if he could.