As to being grammatically correct, ask anyone who does not play dnd to read that one sentence, then ask them if bloodline levels add to character level based only on that sentence.
Two problems with that idea. First, someone who doesn't play D&D won't understand the significance of a lot of what's going on in that sentence or how those terms interrelate. It'd be like asking a chef something about particle physics. Second, that single sentence doesn't encapsulate the entirety of the way bloodline levels behave. If it did, the authors wouldn't have written anything else.
The author said it does not raise character level the way a normal class level does. For that to mean it does raise character level, it needs to do it differently.
True.
If bloodline levels and normal class levels both raise character level by 1, they're raising character level in exactly the same way, not differently.
False.
You brought up the glossary earlier. Check out Hit Dice (
bold mine):
"In the plural form, a measure of relative power that is
synonymous with character level for the sake of spells, magic items, and magical effects that affect a certain number of hit dice of creatures."
Then crack open the Monster Manual and check out Effective Character Level in the glossary (
bold mine):
"A character's ECL is the sum of its
hit dice and level adjustment."
So from this, it looks like your character level is normally equal to your hit dice, and normal class levels increase your character level by adding hit dice (or at least add hit dice in the process of increasing character level). Bloodline levels don't add hit dice, so if they increase character level, it is decidedly not "the way a normal class does", which involves adding hit dice.