That's true as far as 60s -- for example, look at the later seasons of Laverne & Shirley, with the year in a banner at the end of the intro -- they go right up to circa 1967.
Much of Happy Days does in fact take place in the 1960s. However, there was still a lot of inaccuracy regarding hair length/styles and fashions.
In memory of lovely Erin Moran 1960-2017 ~ Missing you
"For you are beautiful ~ And I have loved you dearly ~ More dearly than the spoken word can tell..."
"What's the word?" (Paul Martin) ~~ "I don't want money for nothing." (Timmy Martin) -- Lassie ROCKS! WORD UP
"It's just a dugout that my dad built... In case the reds decide to push the button down..."