PterAnd universal falsehood. What a phrase! This is important because we are not talking about something that is always true. As a result, we can only use the past tense in sentences starting with "I thought it was". The "was" is not the result of backshifting. It is used instead to indicate that the believe was hold true in the past but is now found to be false.
My apologies for introducing a joke! The "universal falsehood" reference is a complete joke! It doesn't matter whether what is reported is universally true or unversally false. What's important is that
in the speaker's mind it is universally (or eternally, if you wish) true. In that way, in the right context, you can even have the reported speech:
The scientist said that the earth is flat.
Consequently, the "was" truly IS the result of backshifting after "thought". It has nothing to do with beliefs considered true in the past but false in the present. You can banish all such logic from your mind. You came to believe some of these things because I put you off the track with my joke.
I don't know which sample sentences you are referring to, but after thought, knew, hoped, believed, and felt, you always need a past tense.
____
I didn't notice that it was not reported speech. (natural, normal)
I didn't notice that it's not reported speech. (also possible, less used)
You may find that each main clause verb has its own idiosyncracies with regard to backshifting. notice acts a little like a reporting verb. What you noticed may still be quite noticeable to your listener, and you may want to emphasize this fact. Nevertheless, keep this is mind: Backshifting is never wrong.
CJ
____
OK. I went back and found these. I think these are the samples you were referring to. The first choices shown are the ones that came to my mind first. It's not really more complicated than that. The second choice is also perfectly grammatical except as noted in the second sentence, where backshifting is required.
My professor said that spiders are (were also possible) insects! I didn't think they were (are not possible). I think he is (was also possible) wrong.
CJ