Requesting a minimum grade ever work against you?
 

Hello, I have a few raw cards that I'm going to submit for grading and was wondering what everyone's experience is with minimum grades?

Does it ever happen where, for example, you request a 3 as minimum on a card that is really a 4 and the grading company just defaults it to a 3 rather than actually giving it a closer look and honest grade?

No, supposedly the graders don't even see the minimum grades until they've been submitted.
Most people don't put minimum grades on raw cards. But those who send crossovers with minimum grades normally get them sent back in the original holders because PSA can't correctly assess the card for flaws already sealed in plastic (and sometimes a mylar penny sleeve). Most will tell you to crack all those out and submit raw, but you're taking the risk that they are altered or minsize, or pressed from screwdown holders and PSA won't declare them anything but "AUTHENTIC / ALTERED".

Why do I keep helping those jacknapes with answering questions about their services?