I've never flown an ACARS equipped aircraft but as far as I know the data "package" sent by the ACARS contains the actual FMC position info.
If its true that the investigators have an ACARS msg reporting certain system abnormalities they must have the attached POS info. They should have a pretty exact last pos to start SAR. But the inital search covered a wide area.
Any explanations?? (Perhaps the POS info was garbled? Or the airplane flew on for long minutes after the first sytem failures.?)