For the record, to copy the \I386 directory from CD to the hard disk is a common practice between techs, since NT 4.0 days, it allows for two rather distinctive advantages:
1) installing from hard disk is faster (due to the inherently faster access rate of the HD when compared to CD)
2) should some more files be needed at a later stage, they are all already on the hard disk, so the user (EXPECIALLY of laptop PC's) will not be prompted to "Insert the Windows installation CD" when some driver of other file are found missing.
I guess that most OEM installed systems use this method as it greatly simplify remote assistance.
With the release of the various Service Packs and Windows Update, the 2nd part of the advantage has of course lost much of it's appeal, unless one makes periodically a slipstreamed-with-all-updates new source and copies it on the hard disk \I386 directory.
WHY some means to automatically update or "slipstream" BOTH source installation files and actually installed files it has not being provided still remain one of the biggest Microsoft "misteries".
As anyone trying to repair a system that has been updated by means of an "original" not-slipstreamed CD has experienced, it is nearly impossible, your best bet is to have another computer either online and with a fast connection or an archive with the various OS and SP's and burn on-the-spot a CD with the corresponding level of update as the system under repair.
jaclaz
P.S.: and yes the name comes from the old NT (cannot say if 3.1 or 3.51) CD where there was a \I386 directory for "Intel" based machines and one for "Alpha" ones, and of course the 386 was the first Intel processor to be able to run (maybe the verb "walk" would be more appropriate) the NT code, 32 bit, more properly defined as "IA-32" or "x86-32" family of processors:
http://en.wikipedia.org/wiki/IA-32http://en.wikipedia.org/wiki/Intel_80386