Given that I mixed up sound/valid at least twice above (bleh), you may have a point…
Still, nothing like a bit of Latin to make it sound like you know what you’re talking about. Argument ad Latinum works as well as the others.
I would say that the unstated premise in the first one is that all the premises are true. That unstated premise is false.
The second one, being the non sequitur fallacy, can have any number of false premises, as long as they somehow connect them. But, if we assume that both stated premises are relevant, then the obvious one is “All people protected by the Secret Service like cookies.” That premise is false.
I remember when I first noticed that all named fallacies can be converted to the fallacy of the (unstated) false premise. It made it a lot easier to identify fallacious reasoning than trying to remember a long list of names (something I am always bad at.)
Unless someone is completely irrational (or intentionally saying something completely irrational), there must be some premise that they are assuming is true that is not.
Isn’t that Argumentum ad Latinum?* 
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*I’m actually clueless on all this Latin stuff so you may well be right. But the joke seemed irresistible.
No. Latin- is modifying the understood lingua. Ablative case, so Latina.
Sometimes the argument is simply irrelevant.
Crane
So does that make the complete correct phrase *Argument ad Latina *or Argumentum ad Latina? English seems to be hard too.
Argumentum. Argument isn’t Latin, it’s English. And we’re doing this in Latin. Or ad Latina. Or something. 
Not a “logical” fallacy at all.
There are indeed Formal Logical fallacies:
What you’re asking for is sometimes called a “Informal fallacy” . Often they are not fallacies at all as the wiki page pointed out: *Appeals to accomplishment are fallacies only when they are simple appeals to authority. It is not fallacious to rely on the testimony of a person who has attained a certain level of education or experience if they can produce further evidence to back up their positions when required.
*
Ahh, but the OP’s issue was anti-appeal to non-accomplishment.
The faulty assertion is that only parents can make informed statements about child rearing, or only motorcycle riders can make informed statements about helmets.
Helmet expertise and riding expertise are different things and possession (or lack) of one doesn’t necessarily imply possession (or lack) of the other. Is there often some overlap? Sure. Is there never non-overlap? Of course not. But the assertion of never non-overlap is the point of failure in the argument.
The inability to correctly construct or read a Venn diagram *is *a failure of logic. Whether that is specifically a “fallacy” or not is a different question.
Now write it out a hundred times. If it’s not done by sunrise, I’ll cut your balls off. Hail Caesar!