Start a subordinate clause with "thus"

Solution 1:

Neither thus nor therefore should be used as a conjunction to connect two independent clauses.

Thus, your example sentences are run-ons. You should use a semicolon to separate the clauses, like so:

I do not wish to offend the grammar gods; thus, I obey their arbitrary rules.

Solution 2:

Your professor has it exactly backwards: replacing thus with whence in the examples you gave results in a sentence that is ungrammatical and incomprehensible. However, thus is not the best word for these examples. I find that all of them read better with therefore:

The substance did not freeze at normal pressure when the temperature dropped below 0 °C, therefore it's not water.

Lisa's evidence does not satisfy the epistemic standard, therefore she don't know that p.

Joel's utterance was offending, therefore his utterance is inappropriate.