You are not wrong.

edit... Just dimes and quarters went through the purity change within the 1967 date. From .800 to .500
And again in 1968 from .500 to nickel. Of course a magnet can sort these since the silver is amalgamated with copper.
The 50 cent pieces(not really called half dollars) and silver dollars were .800 silver in '67 and nickel in '68.
aye... I read above so I'll make a list.
1935 - 1967 silver dollars; .800 silver w copper
1968 - + silver dollars; nickel
1870 - 1919 fifty cent pieces; .925 silver w copper
1920 - 1967 fifty cent pieces; .800 silver w copper
1968 - + fifty cent pieces; nickel
1870 - 1919 quarters / dimes; .925 silver w copper
1920 - 1966 quarters / dimes; .800 silver w copper
1967 - quarters / dimes; mix of .800 w copper and .500 w copper
1968 - quarters / dimes; mix of .500 w copper and nickel
Incidentally, the 1968 nickel composition quarters/dimes may have a higher value than the silvers. I know of no mintage numbers differentiating .800/500 silver in '67 or .500/nickel in '68... 'cuz there are none. The above list is of course for circulation coins. Collector coins and Proofs and such are entirely another matter.