I’m not sure what it is for something to be true to a person. For a person to believe something is for them to take it to be true. So maybe that’s what people have in mind when they talk about something being true for somebody.
But now notice that I can take something be true and just get it wrong. Somethings I take it to be true that my keys are on the kitchen counter and it turns out my belief is just false.
What what I take to be true is subjective. But what I take to be true doesn’t always turn out to be true. Whether my belief that my keys are on the counter is true depends on what is objectively the case. In particular, whether an object, my keys, is located where I think it is out there in the world of objects.