How many miles has your engine done ?
The tappets do contain an internal spring loaded piston to take up play against the valve stem ,creating a space for the oil to fill once the engine runs and it is quite common for these to stick and not allow the oil in .
The only way to determine if this has happened is to remove the tappets , turn them upside down and press on the piston with a screwdriver to see if they have a bit of bounce because some oil has drained out . If they are stuck solid , they can be dismantled and cleaned then soaked in an oil bath to refill them .
So if they refuse to respond to an engine flush , it is not the end of the road !
This video shows it all ......
https://www.youtube.com/watch?v=9geLvfDx4eA