Em no the above is not technically correct.
You can get "pre-amps" for guitar (see Samsamp PSA-1 and Line 6 POD) as well as other insturment. Neither of these kind have anything to do with mics... so saying that it is always a mic affair isnt really correct.
However, what is right is that yes DI boxes are very basic impedence matching devices. A pre-amp, no matter what kind it is, usually has a signal processing quality to it. e.g. most mics preams have a built in compressor, limited e.q. etc