The higher oil price was "a" cause, not the "sole" cause.  Inflation in the 70s was due to expansionary fiscal  (as in budget deficits from war spending and welfare goodies), and monetary  (as in QE to accommodate fiscal overspending) policies.  The effects spilled over to the 70s.  (I did say 70s, in my above comment.  Didn't I?)

Then Tricky Dick Nixon played along because he wanted to get elected again.

Oh, medical costs were rising quickly in the late-70s and 80s because medicare would pay them, almost without question.  They wised up about 10 years later and really tightened up.  I know, because I was CFO for several hospital organizations for about 15 years back then.  Medical programs really expanded, like dialysis, which was paid 100% by medicare.