It seems a stretch to say that James Randi is lying when he doesn't include a disclaimer that the same word happened to also be used for something more scientific around 80 years ago.
Everything Randi talks about is perfectly true if you use the contemporary understanding of the word "homeopathy"
Which he wasn't. He was specifically talking about homeopathy in the period when it was invented and when it came to the US in the mid 19th century. In fact he even talks about 'the proving', which as a far as I know isn't even actively done anymore in modern homeopathy. (I'm pretty sure the modern manufacturers are just reusing old formulas and not actually doing new 'research'.)