Both “going against the grain” and being “on the level” are expressions from carpentry.
When a bladed instrument is used to smooth a wooden surface it only works when applied with, or in the same direction as, the grain, otherwise it’s a mess.
A level ensures the precision of a frame alignment.
Someone that is going against the grain is usually doing things wrong, and so is probably not as trustworthy as someone on the level.
The term “on the level” does not come from carpentry. It’s derived from Masonic history where the “level” is the gauge of a mans journey through life.