Present participles representing actions simultaneous to main verbs

Some time ago my co-worker Mike Harris came upon his mother-in-law's 1919 grammar text, Guide to Composition by James Finch Royster, Ph.D, Kenan Professor of English, University of North Carolina, and Stith Thompson, Ph.D, Professor of English in [sic] Colorado College. This slim, pocket-sized hardback contains 283 points of composition to delight and tantalize the grammarian.

Here is Royster and Thompson's No. 225:

Do not use a present participle unless it represents action of the same time as that of the main verb.

Examples

(Loose)
(1) He entered the university in 1911, finishing in 1915.

(Right)
(1) He entered the university in 1911 and finished in 1915.

(Wrong)
(2) He was an old man now, being born before the Civil War.

(Right)
(2) He was an old man now, having been born before the Civil War.

Note 1. -- A syntactical defense of the not uncommon construction seen in "He entered the university in 1911, finishing in 1915" has been proposed by assuming that the present participle finishing is not adjectival, but that it is a predicate, coordinate with entered. If this is true, we have a loosely articulated sentence -- two coordinate ideas expressed by verb forms of unequal rank.