I agree the English given here is OK. But one could also say (slightly more elegantly): I see her but not him.
The given translation is not grammatically incorrect but I agree something like 'I can see her but not him' or 'I see her but I don't see him' sounds more natural and is more likely to be said.
Although they make the same point -- you see one person, but you don't see the other -- I believe those would be different sentences in Czech... just like they are in English.
Maybe a bit formal or bookish sounding, but I could imagine someone saying it back in the day...