We study several strenthenings of classical circular security assumptions which were recently introduced in four new constructions of indistinguishabilty obfuscation from lattice-based primitives: Brakerski-D\"ottling-Garg-Malavolta (Eurocrypt 2020), Gay-Pass (STOC 2021), Brakerski-D\"ottling-Garg-Malavolta (Eprint 2020) and Wee-Wichs (Eurocrypt 2021).

We provide explicit counterexamples to the {\em $2$-circular shielded randomness leakage assumption} of Gay-Pass and the {\em homomorphic pseudorandom LWE samples} assumption of Wee-Wichs. Our work separates classical circular security of the kind underlying un-levelled fully-homomorphic encryption and the strengthened versions underlying recent iO constructions.