I see their points as essentially being the same. After all, the new advances still include and can describe what occurs in Newtonian physics but they can explain other phenomena as well and do it better.
Another example I like to use is how our understanding of ‘acid’ and ‘base’ has changed over time.
Initially, ‘acid’ was merely something that tasted sour and ‘base’ was something that tasted bitter. Indeed, the German words for ‘acid’ and ‘base’ translate as ‘sour’ and ‘bitter’. It is the same in English, but since they are latin words that were adopted into a Germanic language, we don’t notice it. But, of course, that is a very limited understanding (and it also has numerous exceptions). There are also various pH indicators that we’ve known about for a long time even if we didn’t have the pH scale.
So Arrhenius came along and figured out that acids release hydrogen ions into water whereas bases release hydroxide ions into water. This is clearly a better definition than ‘sour’ and ‘bitter’. We were getting somewhere.
But there was, of course, a problem with that definition. Many things that taste bitter aren’t simple bases with a hydroxide ion. Caffeine, for instance, is very bitter tasting and is indeed basic, but there is no hydroxide ion for it to donate. What is going on? Well, Brønsted and Lowry saw this problem and modified the definition slightly. Now acids were proton donors and bases were proton acceptors. Now caffeine makes perfect sense as a base because it has nitrogens that can accept protons. Since water is a proton and a hydroxide ion, these bases release a hydroxide ion by taking a proton away from the water! All the acids and bases that could be described by Arrhenius were included in this new mix and some new bases were included as well.
However, there were still some niggling compounds that would lower the pH of a solution that couldn’t be described by the BL definition. So Lewis took the next step and defined acids as electron pair acceptors and bases as electron pair donors. All of the acids and bases described by the BL definition and the Arrhenius definition are included in this new understanding plus some new acids and bases.
From there, other refinements have been made about various orbitals and how the molecules behave and, no doubt, further enhancements will be made.
That situations exhibits the same narrowing that Asimov talks about as well as the expansive nature that Putnam talks about. Likewise the shape of the Earth that Asimov talks about can be understood as making the theory ever more applicable as our understanding increases. Same deal with the new physics.
It’s a matter of perspective, but when you actually see the results in action, the two are in fact the same thing.