Yes the proof of this is their hard work and the matches they have won and their points also explain this to us. It is just a matter of making ourselves accept according to the prediction which team will win. I also think it is right because Barcelona is ahead of all the teams with this struggle and it is very important otherwise their fans will be angry and doubt the strength of the team which will be difficult for them for the coming season.
First of all, a team's hard work doesn't guarantee it can get better results. If you remember, Liverpool had very good hard work in several competitions and in this UCL, Liverpool was able to perform very well. But the fact is that Liverpool failed.
Also, the fans do not guarantee that the team will win and qualify in the future. So when you say that the fans will be very angry if the team fails and will not trust the team anymore. That doesn't make sense to me.
At the moment, Barcelona are looking very convincing, but we must also remember that Inter Milan can do anything to fight back with different tactics and beat Barcelona.