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“In a typical hydraulic valve lifter, the plunger automatically adjusts to eliminate clearance in the valvetrain.”

The statement accurately describes the normal function of a hydraulic valve lifter. In typical designs, the internal plunger uses oil pressure and spring force to take up lash and maintain near-zero valvetrain clearance during operation. Manual preload is still required at setup, but that does not negate the lifter’s automatic self-adjusting action once correctly installed.

“In a typical hydraulic valve lifter, the body is the outer casing.”

The evidence supports the ordinary technical meaning of the term. In standard hydraulic valve lifter descriptions, the body is the outer cylindrical casing that houses the internal plunger, spring, and check-valve components. A niche alternate design uses different housing/body terminology, but that does not materially change what is typical.

“In a hydraulic valve lifter, a check valve allows engine oil to flow into the lifter's high-pressure chamber but prevents it from flowing back out when the camshaft lobe loads the lifter to open the engine valve.”

Technical sources consistently support the described mechanism. In a hydraulic valve lifter, the check valve admits engine oil into the pressure chamber and closes when the lifter is loaded, preventing reverse flow so the trapped oil can transmit motion to open the valve. Some designs also rely on oil-gallery port misalignment under load, but that is an added detail, not a contradiction.