"Seriously though, I see on Wikipedia he's credited as the inventor of the pocket calculator. Is this actually true?"
Depends how big your pockets are!
Seriously, no, he didn't invent the pocket calculator. Jack Kirby of Texas Instruments is usually credited with inventing the first portable calculator, but it took a few years, a few iterations and new technology, such as LED displays to get something truly pocket sized. (Kirbys used a paper tape for output!!)
I think the first pocket sized one was in Japan. But, as we see from Sinclairs other products, he was first to market with a cheap and affordable pocket calculator. Much of what he did wasn't new as such, just better and cheaper (if sometimes mechanically a bit unsound!). I don't think he laid claim to inventing the calculator, but some of the press seem to be people who don't do proper research and often credit him as the inventor. Unlike Apple, where the fanbois credit Apple with inventing anything they have success with and Apple do nothing to dispel the myths :-)
Sinclair didn't invent new devices, everything he produced already existed in some form or other. He invented new, cheaper and better ways of creating things that were already possible by doing the impossible so the rest of us could afford to own them. Almost the polar opposite of what Apple has become :-)