The talk of his previous misdemeanours or lack of a 'face' for the 'image', bringing down the transfer only really matters in situations where the selling club needs to sell as they lack money, or they want to get rid of the player.
A transfer is compensation of the selling club for releasing a player early from their contract. I.E. What the player is worth to the selling club for the remainder of his contract. As Liverpool don't need to sell him, and because of what he is worth to Liverpool, for the remainder of his contract, it will be difficult for the buying club to haggle down the price.
If Suarez played for a club which had money problems then it would be much easier to haggle down his price. The rumoured value of Suarez by Liverpool is meant to be a minimum of £100m. And with the Arsenal thing, John Henry has shown his ruthless streak.