Steve, you are right. If David had wanted to take a good picture of the curtains in his house then he would have have white balanced close to the colour temperature of each strobe. But instead he was trying to demonstrate the difference colour temps of light of the different strobes - so chose to shoot on a fixed white balance for all - for comparative purposes.
If each was white balanced correctly then, yes, the colours of the different shots above would look the same. In other words 4600-4800K for the Subtronics and 5400-5600K for the Sea & Seas. Such settings would give you correct looking foregrounds as long as you were close to your subject. (((If you were not close these camera white balance settings would be higher))).
If you are shooting strobe only shots (i.e. macro or pictures of curtains in a dark room, as above) then you will not see any appreciable difference in the colour that results from the different strobes - as long is each is white balanced correctly.
The consequences only rear their head when you shoot balanced light. Because the white balance settings required to make your strobe lit foregrounds appear correct - will alter how you camera records the blue. A white balance of 5500K will record a muddier blue than at 4800K. Have a look at this example image below, same file processed at different WB settings (sorry it is a bit big):

The advantages of a warm strobe are that it allows you to shoot on lower Kelvin value white balances. This will help record richer blues in your photos.
You can also filter cool strobes to achieve the same result. Here are some shots I took while diving with David, to compare the blues I get with and without filters on my Inon (5500K) strobes. The foregrounds should look the same, the difference should be in the blues:

Hope that this has cleared, rather than muddied the waters,
Alex