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Well bach wrote most of his much for the organ, or on the organ.... sooo. We can maybe conclude that he was a BIG fan of the organ, or there were not many harpsichords/clavis at his disposal.

I don't know what the source material for them actually indicates, if anything, nor whether it is the same for each one, but they do seem to be called "harpsichord concertos" quite often. Even the entry on Bach's concertos in Grove refers to them in that way, rather than using the generic "keyboard".

Regardless of nomenclature, is there any doubt that when they were played in public by Bach and his kids, they were in fact performed on harpsichord(s)?

How is that news when its true? Maybe you should do some research like I have.

From what I remember, Bach owned a harpsichord (a large one) and a clavichord, at least.
While much of Bach is possible to interchange between instruments, some of it was specifically written for clavichord (some parts of the Clavierubung have notations to do so), and many of his works appear to have been written for stringed instruments. Of course, he also wrote for organ, as well (he worked for churches, after all!) - but I wouldn't say that the majority of his more frequently-played works were for organ specifically.

In those days, it was the rare individual who had access to a full-blown organ, so much of the music he wrote for his students was probably meant for the more easily available instruments of the time. Organs were expensive and churches usually had them, harpsichords were less expensive but still expensive to maintain, while clavichords were more easily affordable and suitable for the small home and very portable. So try to imagine who he was writing for, what the situation was, and you might be able to make some sort of guess as to a good instrument.

Unfortunately, there is no clear-cut answer as to what works were meant for what instruments, no matter what anyone says - and they have said a lot! Almost every single book on Bach or his musical time tackles the issue, to some degree. This is why many performers choose to record some of his works on multiple instrument types.

There is an inventory list somewhere that lists what Bach owned when he died.
Among them: 2 Lute-Harpsichords, 3 harpsichords, 1 lute, 1 spinet. I think he also had some organ practice pedals or something similar.
This site gives a good breakdown on some of the arguments over clavichord-usage:
http://www.bach-cantatas.com/Topics/Life.htm

It's helpful to know that his son Carl was quite fond of the clavichord and gives us a large repetoire for the instrument, a fondness he probably picked up from his pop.

Yes, they were harpsichord concertos specifically. Harpsichords were very common in those days, to be used for the continuo playing that kept the players together, so they were easily available in such a situation. Whenever you see a work that is from that time, just assume there would be a harpsichord tinkling along in the background, in most cases.

The clavichord, while a lovely little thing, was not suitable for public performance with other instruments, it was a more private, personal isntrument. Of course, we can be thankful that if became so popular, as our modern piano probably owes a lot to it.

.....Bach's organ works DO, actually, outnumber his compositions for other keyboard instruments.....

How do you shape on a harpsichord? Phrasing, articulation. That is minute changes in the lengths of notes and the gaps between notes which provide a "shape" to the music. Nothing to do with dynamics. I would argue that the shape of music on any instrument, including the piano, is more to do with changes in phrasing and articulation than changes in dynamics. Dynamic changes alter the emotional temperature, not the shape.
Quoting Francois Couperin in his preface to his 1st book of ordres:
"Experience has taught me that strong hands, capable of the most rapid and light execution, are not always equally successful in tender and expressive pieces. For my part, I frankly confess that I would much sooner be moved than astonished.
The harpsichord is a complete instrument by virtue of its range and sufficient unto itself. However, as one can neither swell nor diminish its sounds, I shall always be grateful to those who, by consummate skill supported by good taste, are able to render this instrument capable of expression."

Couperin was probably the greatest composer for the harpsichord in terms of writing music specifically for that instrument and no other and he valued expression above virtuosity. Seems to me that he had faith in what a harpsichord can achieve.

THEY DO?
Then I'd give him "credit" on what he said.

It depends on what we mean by "compositions."
If the WTC (2 books) counts as 48, and if we then add the suites, partitas, various stray works like the French Overture, and top it off with the inventions (2- and 3- part), I would have thought the organ works would hardly keep pace, if we're talking about "how many." Even if we mean duration.....I'd think organ would still be lagging.

Mind you, I don't think these "counts" matter for anything.

.....In terms of numbers the organ works win, but only slightly (of course the organ list is heavily laden with chorales).....

AHA!!
You're counting the CHORALES??????

I've never thought of those as organ works.

I know the number of them very well -- "371" is firmly in my mind, and I've had fun doing all kinds of mathematical things with the number.
(It's a great number.)
But I never thought of them as organ works.
I thought of them as, well, pure music.

If the chorales count, it's tough to try to make any kind of point against what Brandon said -- whichever way he meant it.

According to many historians, the Lute-Harpsichord was his favorite instrument.

http://www.baroquemusic.org/barluthp.html

Now what may he have written for that instrument? We will never know. But he owned one!