Not completely true, but he certainly built up a very impressive record (no pun intended) of not just inventing things, but also turning them into useful products and taking them to the market.
The basic idea for a phonograph was described in a paper by a French scientist in 1877, a year before Edison got his patent. He didn’t build a working model however, so for all we know the idea may have languished for another ten years if it wasn’t for Edison.
Contrary to popular belief, he did not (according to the same link) invent the light bulb but improved on an existing design for which he bought the patent from the original inventor. As with the phonograph, what set him apart from lesser men was not so much the creativeness or originiality of his ideas, but the fact that he put in the 10 years of hard work needed to turn that first prototype into a commercially viable product. He famously stated that “invention is 1% inspiration and 99% perspiration”, which was certainly true for his own work.
Still trusting the same link, his inspiration for inventing the Kinetoscope, the first motion picture camera, came from a visit from Edward Muybridge, who was leading the field at that time and is still considered “the father of motion picture”. Edison refused the offer to cooperate however, because he considered that he could develop a more efficient camera by himself.
So it’s not entirely true that no-one else was working on the same subjects, but he certainly did more than his share of the work when it came to the “99% perspiration” part. It’s hard to tell how much longer the world would have had to wait for practical light bulbs and motion cameras if Edison had not been there.
The periodic table was somewhat of a breakthrough and for the most part the work of one man - Mendeleev.
But still wasn’t good enough 
Konghsei (an early Qing emperor) had to rely on the assistance of several missionaries to forge his own canons.
Earlier works tend to be the work of a single person (like the discovery of Radium by Madam Curie) while contemporary inventions and discoveries tend to be “races” among teams.
Velcro? Didn’t change the world entire, but pretty amazing step from annoying little burrs that have been sticking to humankind since we had ape-fur to handy sneaker closure.
With regards to behind the times breakthroughs, I’d have to nominate the Napoleonic-era signal telegraph. This string of semaphore towers could send a message from one end of europe to another in less than a day. An early version of it was based on original ancient (or Dark Ages?) Roman plans for one. So I’d count that as behind its time, yet it enabled Napoleon to hold his Empire together more effectively by being able to pass messages from almost from the Russian frontier to Paris in less than a day.