Fair play, but we are arguing semantics there. I acknowledged that it is a cliche for drivers to say they are "reinventing " themselves for the new season.
No, Nico did not say much about his form, but others did. Which is why I tend to believe he did dedicate himself. The way I read it, it seemed like Nico was just working out more, and studying his craft more. Whether that means he was faster or better is open to debate.
You say Schumi made progress against Nico, why could it not be that Nico digressed in that year in relation to Schumi? It could work both ways. Watching Schumi crash into JEV, underlined to me that Schumi's reflexes were fading fast. I do not take into consideration the years 2010-2012 when accessing Schumi's career, they neither add or take away from his legacy in my opinion.
I actually agree that Hamilton fans used that every excuse going for Nico matching him. Which is probably why the notion gets scoffed at. But the line of thinking that Nico was stepping up his game came long before Lewis and Nico fought on track. It must have been later on that Hamilton fans hijacked it as a excuse (I never actually read any Hamilton fans use it as a excuse, but I will take your word for it)
There was a trend, I did not discount the opportunity Rosberg would have beaten Michael in 2013, I see a case he is beating Michael quit handy in qualifying but not in the race, they were close since 2010. But I see no big swing in favor for on of the drivers, because the basis of the car were the same..
The excuse was overshadowed by the breaks and chassis things, it was used quit often, at the beginning of the season, I believe both Schumacher and Rosberg were top five material that time, and if we change Schumacher with Rosberg, if Schumacher would have matched Hamilton, the crying would be louder, but if you look it that way he was in a new team, couldn't adapt to the new breaks against a top driver. People believed Hamilton would trash Rosberg because, he was the guy who was matched by the over the hill driver the season before. The exception was wrong, if you believe Schumacher/Rosberg were mediocre, you were disappointed or you tried to fix what you thought about Rosberg, if you believe they were one of the strongest pairing on the grid, like Ross Brawn, Lewis had a good first season. The Mercedes car was tricky, we have seen it in 2012 and 2013, with abysmal performances for all drivers. I see it that way, Hamilton had his troubles, because of the car, and he couldn't drive to the max against a top five driver, likely it will change this season.
To answer in this context the question: 2013: Car was not good enough, 2014: good chance against Nico, but would have been hard and close, 2014 against Lewis: no chance