The חפץ חים clearly says that the issue with praising in oublic is that people will say something negative.
It’s more likely that the author of the English sefer meant that than misunderstood the חפץ חים.
In the edition with הגהות, it says that based on the reasoning, if in fact the speaker determines that it won’t cause anyone to speak negatively, it is מותר if not excessive.