Solubility in different pressure conditions
As noted by Wikipedia, 


  "Henry's Law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid."


So you are absolutely right. 4 times the pressure of oxygen should result in 4 times as much oxygen being dissolved. 

The answer key for the problem must be wrong.


  User Delta_G made an interesting observation/correction. The problem is asking about the volume of gas that dissolves, not the concentration of oxygen in the water. So 28 ml at 4 atm of oxygen gas contains four times as much oxygen as 28 ml at 1 atm of the gas. So in either case 28 ml of the gas phase dissolves into the water.