Split infinitives are an old chimaera of English grammar. Actually, it is not true that it is illegal to split infinitives in English. To quote the Chicago Manual of Style , "Although from about 1850 to 1925 many grammarians stated otherwise, it is now widely acknowledged that adverbs sometimes justifiably separate the "to" from the principal verb." (5.106) ApJ , as a modern journal, is happy to concur.
English has a strong preference not to split transitive verbs (such as "confirm") from their objects ("the result"); in particular, transitive+object pairs should not be interrupted by adverbs ("empirically"). The copyeditor could also have fixed this sentence by moving the adverb to the end, rather than the beginning ("to confirm the result empirically"), but having adverbs precede rather than trail verbs is a more vigorous style.