How are you distinguishing between Giffen and Veblen goods? If you define Veblen in such a way that all Giffen goods are Veblen and then say that disqualifies them then of course you'll find there are no Giffen goods.
> To be a true Giffen good, the good's price must be the only thing that changes to produce a change in quantity demanded. A Giffen good should not be confused with products bought as status symbols or for conspicuous consumption (Veblen goods)
Veblen goods = Goods for which demand rises with price because they are status symbols Giffen = Goods for which demand rises with price - Veblen Goods
However there are no examples there that hold, to me this signifies that the only goods for which the law of demand does not apply are status symbols.
No, it's an inferior good (in the economic sense) in which the (negative) income effect of a price increase outweighs the success substitution effect.
What you are describing is a good that has a positive elasticity of demand with respect to income (or, technically, two different goods, because the higher price represents a different good altogether - one with a higher status symbol).
The idea is that the good is the lowest quality way of fulfilling some need - so people buy it because they can't afford anything else.