I think that it depends on yur definition of "crap oil"
In short
A quick dry vs a slow dry would have more of an effect on an alcohol extract, the negative qualties of a quick dried bud dont really carry over
Fresh frozen retains more terps etc, flavorful compounds with some medicinal benefits, some strains are a bit disagreeable if done in this manner...to explain, during the slow dry of the "cure" polycyclic aromatization and oxidation of terpenoids alter the flavor profile, its more robust with a lower ppm sensory threshold, smelling much stronger. Its less perfumey floral even soapy or "green" from corresponding aldehydes and ketones being altered and volatizing away
The curing of the plant itself can effect your oil as does the moisture content. For example using fresh frozen material will green up a qwiso extract in a minute to the same degree fresh dried herb would in 24 hrs. Its much harder to make a quality product in this manner, even if superior in my opinion.The actual curing of the plant itself reduces nitrates sugars starches and chlorophyll, this gives well cured bud its characteristic smooth smoke. These compounds can carry into your extract
Now your wanting to go bho which is a good bit less polar than an alcohol extract obviously, it will extract less of these compounds
The medical benefits in cannabis come from the diverse compounds found inside. Cannabinoids and terpenes playing the biggest role, these would be things like thc (and the propyl) thcv cbc cbcv cbd cbdv and many more..the terps would be things like myrcene caryophyllene linalool etc
Drying the weed means you lose a majority of the water, which is in relatively much higher amounts than terpenes that can have a low boiling point..this means take away the water, take away some terps..then you still have to purge the solvent from your extract..obviously some compounds with a higher boiling point are also reduced during this process
This will raise cannabinoid concentrations..at a cost though
Now a quick dry implies higher heat, more airflow, lower rh..basically the faster you dry (evaporate), the higher the proportion of higher boiling point compounds are being lost as well.
All these things may not even be evident to someone who doesnt do this "professionally"
The common hay smell or whatever wont carry over, for the most part since your removing the trichomes everything associated with the plant stays behind.
technique plays the biggest role no matter what. And you could have the best material, done a pefect extraction and screw it up while purging.
As to the last post about wet weed and runny oil, i think goopy lol is more appropriate, hash oil filled with terps is wet and delicious looking due to compounds with a low melting point. "Runny" generally has a negative connotation in these circles but thats a whole nother long subject