I think you would have to make a statement about his role before we can make a judgement about if it is exaggerated.

He was an extremely influential figure at the time. He was in all likelihood the richest individual in North America when war broke out. He led Virginia's delegation to the first colonial congress. And Virginia was the largest, richest, and most influential colony at the time. Imagine if some combo of Bill Gates, Warren Buffet, Robert Downey Jr, and Paul Ryan showed up at the head of the delegation for the superstate of Cali-Texas and you'll get a feel for how he was viewed at the time.

And while he did have some military experience, it is no doubt for his fame and influence that John Adams nominated him for supreme command of the colonial forces. And that appears to be a great choice. He was a mediocre tactical general. But he was a fantastic leader. His poorly fed and equipped men were fanatically loyal to him. And his French advisors were impressed with their discipline, on the march and in battle (less so in camp). He was a good organizer and he made the best use of what he had. And he was a canny politician. He played to his audience back in congress very well. And his long term strategy of playing "Fabius" and avoiding full scale battles where he could be wiped out, and basically continuing to exist, proved to be a winning one.

Later as the President of both the Constitutional Convention and then the US, he acted admirably. I think today we would think him unimaginably restrained. But he was trying to rise above the fray of the politics and keep the office of the President (and himself no doubt) unsullied by politics. But he was exceptionally well respected at the time. Remember he was elected and re-elected unanimously. And there were plenty of qualified candidates like Adams, Jefferson, and Madison hanging around to choose from.

And of course the US owes him a huge debt simply for the act of stepping down after two terms as President. There was no expectation to do so at the time. And in so doing, he established a vital precedent that held for nearly 150 years.

In all I think Henry Lee still put it best at Washington's funeral, "First in war, first in peace, and first in the hearts if his countrymen." He didn't win the revolution alone. He didn't establish the country alone. And it is likely it all would have happened without him. But he led throughout the process and worked tirelessly to make it happen. He was a remarkable individual.

For an intro biography I would recommend: His Excellency: George Washington by Joseph Ellis

And I would also recommend: 1776 by David McCullough. It covers that pivots year and highlights most of the major players.