As a hypothetical classroom exercise in public choice theory what they propose is totally fine. They ask, if an agency with responsibilities for (1.) building statues of Benedict Arnold, or (2.) providing medicine to children has to cut its budget, what will it cut first? The answer is the medicine because that will cause the public outrage to get the funding restored.
It's fine as a hypothetical, and the extent to which it describes real bureaucratic behavior is an empirical one (and a reasonable empirical question to look into), but don't let them trick you into misunderstanding what sequester does.
With very few exceptions, the administration has no latitude for shifting around what it cuts. In its report on sequester, the OMB writes:
"The percentage cuts in this report, and the identification of non-exempt accounts, reflect the requirements of the laws that the Administration is applying. With the single exception of military personnel accounts, the administration cannot choose which programs to exempt, or what percentage cuts to apply. These matters are dictated by a detailed statutory scheme. The Administration does not support these cuts, but unless Congress acts responsibly, there will be no choice but to implement them."Later in the report they discuss the fact that the parliamentarian of the Senate agrees with this interpretation that there are no rules in the act allowing shifting of the burden across discretionary budget accounts (of which there are apparently over 1,200 that have to take the same hit).
If you skim the appendix and look through all the different accounts it's clear that the special exemption rules indeed apply to very feew accounts.
Now, given these stupid policies is the administration making the stupidity of it all very public in the hope of doing something about it? Of course. That's what I'd do too. That's what I've done to a certain extent on this blog. But what they're not doing is deliberately cutting the most sensitive stuff to get a reaction. They have to by law.
It's bad enough that we have the sequester in the first place. I find it disgusting that economics professors are either distorting what's going on or even cheering it.