Can any of these sites actually realize that in actual USD in a reasonable timeframe? How much time and effort and waiting does it take to see $11k in their hands? Or do they have to do transactions of $100/max once per week with a waiting time of 10 days each?
Daily DOGE trading volume is in the hundreds of thousands USD equivalent. Selling $30k worth is easy.
Check the order book for just one exchange (Cryptsy DOGE/BTC). Very liquid. There are tens of millions of DOGE worth of open buy orders at any moment time.
https://bitcoinwisdom.com/markets/cryptsy/dogebtc
You can buy however much people are selling. I bought up to $2000 of Dogecoin at one time. I've regularly seen orders for significantly more than that though. The transaction itself is instantaneous, but of course wiring the USD to the exchange took 48 hours.
The timeframe is how long an ACH transaction to your bank takes. Almost all exchanges have daily and weekly limits, ranging from $4,000 - $10,000 a day but they will often up those limits if you give them more personally identifying information.