I think that meter must be off. Camera shouldn't have problems getting light, just the meter.
Perhaps there's something corroded. A rusty cable or contact can be a problem, with their reduced capacity. At worst it might be a problem of the meter cells.
A low tech test for meters that I perform on my OM-1 is pointing the camera at a completely blue sky of noon, and see if it isn't way off the sunny 16 rule. As you describe it, it isn't just a little bit off, it's completely out of calibration.