No, they are not correct.
LCMS District Presidents perform neither the function of a bishop as defined in/by the New Testament (a pastor) nor the function of diocesan supervisors, as occurs with the "bishops" of the papacy. LCMS congregations do not "belong to" districts of the Synod; rather, districts are made up of autonomous congregations, as is the Synod itself in the pure sense (would that it were the only sense).
Knowing these distrinctions is table stakes for this conversation. This is not weird. If you find this state of affairs embarrassing, that is an indictment of you and your ignorance. Read Elert, Eucharist and Church Fellowship in the First Four Centuries. It may help. No, there is no audiobook.
Nor are LCMS District Presidents the civil-ecclesiastical servants of a Christian prince, as was the case in Post-Reformation Germany and, whether they'd admit it or not, in the Evangelical-Lutheran churches of Scandinavia.
"But my heckin' Chemnitzerino and my vaporwave Bo Giertz memes and Lithuanians with croziers!"
Just stop. Chemnitz and Gerhard and the rest of the Lutheran orthodox fathers would not know you. C. F. W. Walther exposits what the doctrine of Chemnitz and Gerhard et al looks like when applied in an interregnum, and there is no material difference between Kirche und Amt from what Luther taught or what the Confessions uphold. None. There has been no "development of doctrine" here, nor can there be. Doctrine is one. Whether explicitly confessed and boldly embraced or implicitly accepted, even if only latently and with a confused and anxious mind riddled by doubts, the exposition of the duplex locus of Church & Ministry exposited by Walther is the Christian position, full stop. And it is inseparable from the right confession of the Gospel in all its articles, q.v., the Book of Concord. No one who wholeheartedly and consciously disavows what is taught in Church & Ministry on the basis of the Scriptures will remain a Lutheran. He will either wear the Lutheran name like a skinsuit (see: the majority of the LCMS "clergy roster") or he will stop pretending and go be gay somewhere else.
A false understanding of Church & Ministry undermines and unravels every other article, including, above all, the chief article: justification. I have said it before, and I will say it again: Walther's Church & Ministry was deliberately retconned in its recent new translation in order to obscure all of this as much as possible. Receipts in the replies.
But I digress.
LCMS congregations do not belong to the LCMS Corp. They exist by divine right, and if, say, the LCMS gets sued under RICO statues and dissolves (God grant it), they will still exist. (Plenty of them wouldn't even know it was gone.) LCMS District Presidents as such have no divine call. Zero. Or rather, they have just as much of a divine call to their work as you do to yours, whoever you are. You pick.
A corporation does not issue divine calls. Pastors do not receive an indelible character at ordination which enables them to issue calls as a group. All such notions are false, fake, gay, and papistic (but I repeat myself).
An LCMS Distict President is not the pastor of the congregations that make up the district to which he is assigned. He is a regional manager serving the interests of a domestic non-profit corporation in Kirkwood, MO, whose entire MO (pun, get it?) consists of mediating relationships between "Synod" and its voluntary "members" (congregational and clerical/professional). 100% corporate hireling, 0% episkopos. Along a different axis: 50% union rep and 50% psychotherapist (exact percentages vary by man). There is yet one mohr axis, but we won't talk about it here.
Calling LCMS Corp District Presidents "bishops" would be the gayest of gay farces. In other words, it would be perfectly in line with the LCMS, and though it didn't fly this time, I'm sure they'll get around to it eventually - maybe by the time the second edition of LLCACA is released.
The Zoomers in the LCMS are correct in saying that the use of the secular titles “District” and “District President” are used for no other reason than “bishop” and “diocese” sounds too Catholic, and the boomers don’t like that. This is not sufficient warrant to break with tradition.