This is not true in the 5.5E rules. The rules on Line of Sight don't mention cover at all and the rules on Cover don't mention being able to see through or not see through it at all. These are two completely different things in the 5.5E rules and nowhere in 5.5E does it say that cover blocks sight or that you can not see through cover.
Also, the method in the DMG for using lines to determine Cover and Line of Sight between two squares on a grid are different. Line of sight is determined using one line from one corner of one square to any part of the other square (side, center, anywhere). Cover is determined by measuring a line from one corner of one square to all 4 corners of the other square.
They absolutely do make a very specific distinction between seeing and having cover. These two things in different sections of the rules. Saying Cover and Line of Sight are the same thing in 5.5E is like saying Weapons and Spells are the same thing; they very much are NOT the same thing.
Line Of Sight is one paragraph on page 45 of the DMG, and that paragraph does not mention cover at all. This is the only place Line of Sight is mentioned at all AFAIK. Cover is detailed at least 4 different places in the PHB and the DMG and the sections on cover do not mention Line of Sight or seeing the target at all.
A Window or a Stone wall, or an invisible creature, all provide cover, but you can see through two of those and not the third. All three of those things can provide cover, but only the Stone Wall can break Line of Sight. That the rules don't explicitly say you can see through transparent cover is meaningless, because that is the definition of transparent. The rules also don't say you can see through air, but you can!
The rules on cover don't mention transparent or opaque cover because sight is meaningless for cover. The rules on Line of sight do mention things blocking vision, because that is what matters for Line of Sight. For example the rules on Line of Sight mention fog specifically, and it is because Fog breaks line of sight, but it obviously provides no cover at all.