In practice, all of us have goals, some of which conflict. This is no less true of oil executives than it is of everyone else. It might well be the case that a certain belief best contributes to a goal that I have but not to the full set of goals. For instance, the executive may want to leave (usable) property to their grandchildren or endow a museum or whatever.

But the answer to your last question is definitely yes. I have lots and lots and lots of false beliefs that simply aren't worth the trouble of rooting out: it would be actively irrational of me to invest the time it would take to find them. In fact, I'd have fewer true beliefs if I tried. That much is mathematically demonstrable. (Take a look at the literature on satisfisizing as a maximization strategy.)

More broadly, though, yeah. A parent believing that their child is particularly adorable or talented might lead to a better relationship than would a more clinical belief set. If you belief a closer relationship to be a valuable thing, then you probably should hold the beliefs you need to form it.

Of course none of this is all-or-nothing. ("Belief the very best thing about your children or you'll die alone.") The point is just that evidence captures only one very narrow dimension of the the things we are doing when we believe.