[paul cotter (OP)]

Anticoagulant  therapy reduces the chance of blood clot formation and does not result in "blood thinning". Yet this spurious description seems to be almost universally used. Actual blood thinning just might have some value in conditions like polycythaemia vera but otherwise it would have a negative effect on oxygen bearing ability which could be disastrous for a compromised patient.

[evan_au]

Perhaps if you describe the process of blood clotting as "blood thickening" (and eventually becoming solid)...
...then you might describe something that inhibits blood clotting as "blood thinning".

Many of our medical terms have been around for centuries, and are not technically accurate, but everyone uses them, and they are generally understood - and that is the purpose of communication.