In 1960, 60 years ago, the noted and eminent political scientist James Neustadt wrote the book "Presidential Power". A book of analytical history, the qualitative work from this book was so convincing in its conclusions, that it is still assigned today for anyone studying American government and the executive branch in particular. A second edition, with more data, is nothing but confirmatory. It's the "default" take on the American presidency for anybody looking past the so often wrong conventional wisdom that the American president is the most powerful man on the planet. So what are the conclusions?
The short version of the book is this: "Presidential power is the power to persuade."
That's it. For all the pomp and circumstance, the fancy jet and men with guns to protect him, the deferential treatment...even the ability to lob cruise missiles now and again, the president has very little actual power.
Presidents need to bargain to influence other branches of government who have their own agendas and base of power. Further, presidents, despite a theory of a unitary executive branch all working for the president as boss, must bargain to influence the executive branch bureaucracy.
Cabinet secretaries (often former primary opponents), agency heads who are career paper shufflers, all have leverage that they can use against the president (leaks, slow walking orders, outright defiance, among other things) and all these require presidents to persuade anyone who he wants to implement policies. Not to mention he has no power over courts, and he could have a backstabbing vice president. Historical examples abound of all these things, starting with George Washington.
So, whenever someone says that "oh, X president was in charge when Y happened" like that means that a man with a thousand demands upon his time handles every little squirrel that runs across the lawn, it shows that they don't know what they are talking about.