IANAEconomist (but I could play one on TV)
It is simply not true that that a good must be "inferior" to be a Giffen good (unless you adopt a special meaning of inferior, which since it's not necessary to do, I won't agree to). The classic example (thought experiment, without regard to whether it actually happened) is potatoes in poverty stricken Ireland: a poor person's diet would be mostly potatoes (inexensive Econ-Utility (compared to steak): calories, fills the belly) with some meat a few meals a week (expensive Econ-Utility: protein, iron, B vities, tasty, "not potato", even a touch Vebleny)
So, arbitrary budget example, let's say $20 at the grocery gets you $15 potatoes every day and $5 of steak 1 days a week. If the price of potatoes goes up, you need to reduce something, but you need to eat every day so you can't reduce potatoes, so you reduce your steak consumption, but now you have some extra money which you spend on even more potatoes. Price of potatoes went up, consumption of potatoes went up. So, potatoes are not "inferior" to steaks, both are requirements for a balanced diet; I supposed a technical econ-definition of inferior could be designed to mean something along the lines of "inferior is defined to rule out your example, aaight"
In any case, while Giffen goods probably can't exist in a market for any length of time, the concept is completely understandable as a short-term reasonable thing that occurs: I go to the store with cash intending to buy an "assemble your own" burrito with guac, the price of beans went up, I don't have the cash at hand now to get the guac, but it's not a burrito at all without the beans, so I leave out the guac... but turns out by leaving out the guac, I can get a larger size burrito: consumption of beans just went up at the same time as the price. This effect happens for sure... does it happen enough to counteract the people who would leave out the beans and keep the guac? Can the "substition of beans for guac" function always be seen seen to be continuous and differentiable? that make beans not a Giffen good? ...
my point is, the way you guys are arguing this is leaving too much out, can't be answered and wikipedia at this level of analysis is too unreliable.