My English grammar book simply says that, after a ditransitive verb (which takes a direct and an indirect object), the indirect object can either come in a prepositional phrase after the direct object ("She told something <to me>") or directly after the verb ("She told <me> something"), implying that the relevant bit of the yacc code for English looks like this:
verb-phrase : ditransitive-verb direct-object preposition indirect-object | ditransitive-verb indirect-object direct-object | ... ;
That doesn't seem to be a general rule, though. Maybe I need a better grammar book!
Your etymological explanation makes sense. Thank you!