Yes, this stereotype of innovation or invention being driven by rich dilletantes is absolutely false, and comes from a marxian historical analysis where the adherents didn't want to acknowledge that drivers of innovation for the most part were from the same background as, uhh, Marx himself, rather than from the nobility.
It is also a dismissive attitude of the incredible obstacles that scientists and inventors had to overcome as they tinkered in garages, rising before dawn to conduct controlled experiments on plots rented with money that should have gone to pay for necessessities, spent family savings on acquiring books, and devoted their lives to improving the human condition, merely to brand them as dilletantes who never had to work for a living.
Sure, wealthy aristocrats were over-represented but were a minority among the ranks of famous engineers and scientists. Most were of modest means, the sons of schoolteachers, reverends, carpenters, iron mongers, small shopkeepers, etc. Innovation is the child of the bourgeoisie.
* George Green (1790s-1840s), of Green's theorem fame, grew up in modest circumstances -- his father was a baker and he worked at the bakery when he was young in order to support himself.
* Benjamin Franklin (1700s-1790s) grew up in a family with modest means -- his parents could only afford 2 years of schooling and he worked on various odd jobs to support himself before achieving fame.
* C. F. Gauss (1770s-1855) - perhaps the greatest mathematician of all time -- was born to poor, working class parents. His mother was illiterate and the date of his birth wasn't even recorded.
* Isaac Barrow (1630s-1670s) -- was born into a middle class family, the son of a linen draper.
* Isaac Newton (1640s-1720s) -- his father became wealthy but then spent all the money and died before Newton was born. His mother had to give him away to his grandmother and when she died Newton lived with the family of an apothecary. Unfortunately he was passed around. Newton did attend some elite schools but he did so on scholarship.
* Thomas Newcomen (1660s-1720s) - inventor of the first successful steam engine -- was an iron monger and lay preacher, as well as an elder in a baptist church.
* Bartolomeo Cristofori (1650s-1730s) - inventor of the piano -- was a commoner who grew up in obscurity, worked for luthiers, and got his big break when he was hired to fix the musical instruments of the Medici family.
* John Shore (1660s – 1750s) - inventor of the tuning fork - was a professional trumpet player
* Daniel Gabriel Fahrenheit (1680s-1740s) - famous physicist and inventor -- worked as a merchant in Holland - as bourgeoisie as it gets!
* John Kay (1700s-1770s) - inventor of the flying shuttle which helped kickstart the British textile revolution - came was the son of yeoman farmer, and apprenticed with a hand loom reed maker.
* Pieter van Musschenbroek (1690s-1760s) - one of the co-inventors of the Leiden jar -- was the son of an instrument maker.
* John Campbell, (1720s-1790s) - inventor of the sextant - was the son of a minister, and worked as an apprentice to a coastal vessel, then enrolled in the Navy, then was promoted to master's mate.
* John Dolland (1700s-1761) - inventor of the chromatic lense - was the son of a silk-weaver and worked as an optician.
* John Harrison (1690s-1770s) - inventor of the marine chronometer -- was the son of a carpenter and had no formal schooling. He also worked as a choirmaster.
* James Hargreaves (1720-1778) - inventor of the Spinning Jenny - was the son of an illiterate hand-loom weaver, and himself worked as a weaver and a carpenter
* Joseph Priestley (1733-1804) - scientist, natural philosopher, inventor (of carbonated water), discoverer of Oxygen, theologian, and author of over 150 books, was born to a large family of cloth finishers. He was also passed around to relatives. He worked all his life as a schoolteacher.
* Richard Arkwright (1730s-1790s) - developer of the spinning frame and pioneer of the industrial revolution - was the son of a tailor (although he died a Queen's knight). His parents could not afford to send him to school so he was tutored by his cousin.
* James Watt (1730s-1810s) - inventor and industrial age pioneer -- was the son of a shipwright and ship owner. He worked in his father's shipwrights.
* Samuel Crompton (1750s-1820s) - inventor of the spinning mule - was the son of a groundskeeper. His father died, when Crompton was a young and spin yarn to make up for the lost income, and that experience led him to develop the mule, which he worked on secretly at night.
* Henry Cort (1740s-1800s) - inventor of the steel roller and many other iron refining innovations - while there are no records of his birth or family, he first appears working for the Royal Navy as a paymaster.
* Andrew Meikle (1710s-1810s) - inventor of the threshing machine and contributor to the Rotherham Plough, he helped spark tha British agricultural revoluion. He worked as a millwright.
* John Fitch (1740s-1790s) - inventor of the steamboat - received little formal schooling, the occupation of his parents is unknown but he worked as an apprentice to a clockmaker.