Regardless of the price of the 70-300 non-L , they've already got a poor performing, long reaching, 75-300mm, and want a step up in quality. They don't need a second sub-par lens in the same focal length range. What they need a good solid lens (and a sucker to buy their old lens! )

With their existing lens they can answer the question of if they want/need over 200mm, and whether they use over 200mm more often than wishing the lens was a bit faster. Given the original budget, we can assume the 70-200mm f/2.8L IS USM II is out... though the f/2.8 non-IS might fall in the accepted higher price range too, just to confuse matters further.