Exactly. Shannon could have called his metric a 'Logarithmic measure on probability spaces', but he chose to call it 'Information' -- even though it's not exact

Exactly. Shannon could have called his metric a 'Logarithmic measure on probability spaces', but he chose to call it 'Information' -- even though it's not exactly what we mean when we talk about information informally; the inspiration and analogy was very important to the work (personally I'd have called S 'Average Information', but that's with hindsight).\* As long as you clearly define and state things (definitions) and can separate the context-specific [technical] meaning from general usage, I find it's a very good strategy not only for popularization purposes but to inspire and draw some valuable intuition from our daily lives into technical matter. Naming things in the sciences is an art :) *: It should be obvious I don't love the usual term 'Kullball-Leibler Divergence' in place of 'Relative Information', although in this case the names are obscure and difficult to pronounce enough to give it an air of rigour and nobility.