Sounds like an urban legend to me... (I've actually hand set type and printed using a hand press). We're only talking a handful of words with the dropped 'u' and infinitesimal costs for both the labor or setting a single letter and it's practically impossible to express just how sub atomically small the extra cost of ink is. (Even in the era when ink was mostly produced by hand.) One can also take a look at the word music - commonly spelled musick in both countries... And both countries have dropped the 'k'. Or, we can look at glamour, where the US has retained the 'u'.
The real story is this: In that era, spelling was not standardized and was still very much in flux. Webster was influential in setting American spelling, and his chosen spellings came to predominate in the US. Johnson became influential in British spelling, and his chosen spellings became predominant in the UK (and by extension, throughout the Commonwealth). Why did they choose different spellings? You'd have to grab a time machine (or make friends with a Time Lord) and ask them.