Baines went down too easily when there was contact. This has crept into Baines's game since he got into the England team, which isn't surprising really.
Ferguson encouraged his players to dive or as he called it, 'we will not win the Champions League until we play like the continentals'. Manu players would go down easily around the penalty area so as to get a free kick for Beckham to get a chance of a goal. This became part and parcel of the tactics that England adopted, and was used to great effect that got them goals and qualification for tournaments. This still goes on with England and Baines is caught up in it.
As far as Sky Sports are concerned they want and need Liverpool in the Champions League for the revenue they bring i.e LFC fans getting sky, selling the rights, and viewing figures when LFC are in it, worldwide. Sky can negotiate better deals when LFC are in, rather than when they are out. They have a vested interest in promoting LFC, that is one of the reasons there are so many ex Kopites on Sky's live games.
Sky Sports have chosen to have a go at Baines dive because we are challenging them for top 4, same last year with Spurs and Bale, they were challenging the RS for top 4. The RS media used Bale to deflect attention from Suarez. Wait until the world cup and when Suarez dives and simulates injury against England, let's see what the reaction of Lineker, Murphy, Shearer when a dubious penalty means Uruguay beats England. Let's see if they say, 'he has the right to go down if Hart is so stupid'.