Or, as Dr Malcom would say: life, uh, finds a way.
This should be a crucial piece of information about the tree laws, yet it's not mentioned in the Wikipedia article about the three laws [1], which is otherwise quite detailed. Reading this, everything makes me think that it was not a parody. I didn't feel like it was parody when reading the Robot series neither. He wanted an alternative to the Frankenstein plot where robots kill their creators and the three laws were part of the answer.
I think the strongest evidence is that many other examples of Asimov, especially short stories are cautionary and deal with hubris and unexpected side effects.
However it's funny to ask for 'evidence' about fiction in the context of "parodying rationalists". no? Since what would count as evidence? Another, more "authoritative" literary interpreter saying the same thing? Maybe a long time ago - historical statements seem to carry more weight, as if people were wiser back then?. Or Asimov himself? But don't they say, only bad writers explain themselves?
Interestingly, this continues to be the case even when the author states his intent plainly. Jonathan Blow's "Braid" is a great example of this: there are several different readings of the story, despite Blow openly talking about his intended meaning.
(I would argue that a text that only allows a single "correct" interpretation is an instruction manual, not a work of art.)
The statement that kicked this off was not a statement of interpretation, but a statement of fact: "Asimov wrote the three laws as a parody". This is a statement that has a true or false answer. You are free to interpret the story as parody and to try to find evidence in the text and use that to argue your point, and that is a perfectly valid way to interpret the stories, but tells you nothing on Asimovs initial intentions.
If you are going to say "The artist intended X when creating this work" then you're going to need evidence beyond the work. Just like there is no one right way interpret a work of art, you cannot use a work of art in isolation to 'prove' artist intent.