Some of the sellers set up automatic rejections unless the offer meets a certain level. Those are easiest to lowball, as you don't even get a real response from the seller, just an automatic rejection. If the offer has to be reviewed, there is a small chance the seller could take offense and email you with less than polite comments. Then again, it's just an email. Delete it and move on.
I offer prices that I think are reasonable, regardless of the BIN price. Often those are inflated in hopes of you offering less, but paying more still than the seller expected. If you think a card with a BIN of $100 is only worth $25, then by all means offer $25.