The most we could say is something that is apparently similar could have a similar origin. To claim that they have the same origin is more precise and would require additional evidence. By specifying the type of lawgiver, you have excluded all other possible types. Such an elimination of options would require additional evidence.
So we can infer things by analogy, but only what you arbitrarily decide we can infer.
Where, exactly, is the line of delimination between "vague" and "more precise" were evendence magically becomes neccessairy where it was not before.
Can we infer that the laws of nature must have been written down before they went into effect, like all other laws?
Consequently, the justification for ascribing intelligence to the lawgiver is purely subjective.
Your hypocracy is astonishing, truely.
Analogies do not support conclusions. The sun is bright like a light-bublb doesn't mean it's also powered by electricity; the computer is red like an apples doesn't mean it's grown or edible.
That a houseplant and powerplant are both "plants" has no relevence; nor does the fact that the mathmatical equasions describing reality are called "laws" as well as the rules passed by people to control behavor mean that they are similar.