(I deleted my initial answer. Sorry, I missed your whole point!)
IMO lot of old theory books have this kind of unclear language.
One way to make sense of it is the general wording "we should take care not to..." is illustrated with #257 - just to show what we are to be concerned with - then the more specific point is made about bass and upper voices and #258 illustrates good and bad.
Bars 4 and 5 of #258 seem to contradict the "take care not to employ" direction of section 88. The only sense I can make of it is it doesn't say "never use..." It's not an outright prohibition. If I try to make sense of it, I imagine it means something like "take care when combining a pitch in one voice with its chromatic alteration in another voice, don't do it indiscriminately, avoid altering the third or fifth, avoid placing the alteration in the bass." That's my sense of the words in combination with the musical illustrations.
If the wording was...
In order to avoid disagreeable tone-combinations we should take care
when employing simultaneously in different voices of a chord a tone with one of its chromatic alterations, especially where that tone
forms the third or the fifth of the chord. Specifically a chromatic
passing note should not be used in the Bass when the Bass tone is
doubled in an upper voice.
...and if #258 bars 4 and 5 were labelled acceptable, I think it would all make sense. #257 merely shows the cross relationship of concern and #258 are specific example of good, acceptable, and bad. (Italics for the wording I changed, which isn't much.)
Keep in mind it's a 1900 translation from German into English. We probably should consider some finer points of wording were not perfectly captured.