It’s possible there are tiny bits of superconducting stuff at room temperature which connect into bigger and bigger bits as temperature drops, until it starts working as a whole at 110K.
Unless the "low quality" part is actually causing the superconductivity. Remember the multiple simulations that showed Cu replacing Pb at a less favorable site (energetically) was better for superconductivity than at a more favorable site. It's possible "high quality" samples actually have less "imperfections", which seem important for the superconductivity.
Exactly it's quite possible that 'worse' is actually 'better' and vv. I'm sure that it won't be long before that will be resolved though, this is all happening so fast that such important answers will be sought by more than one team.