ANSWER: You are right -- if the Court had decided the case on due process grounds. But that sentence in our casebook was really an aside. If you look at the full opinion, you will see that the Court decided the case based on the Equal Protection Clause. The statute (at least in its application) discriminated on the basis marital status. The Court subjected this discrimination to rational basis review, and held (perhaps disingenuously) that the law failed to rationally further a legitimate state interest. (More candidly, I would call this rational basis "plus," as the Court was certainly more demanding than the test of Lee Optical.)
QUESTION: What level of scrutiny applied in Griswold? We think it's strict scrutiny because our notes say "high level of scrutiny" and again it concerns fundamental right to privacy.
ANSWER: That seems like a logical inference to me. The Court does not use the magic words, but yes, I think it was applying strict scrutiny.
QUESTION: What are the strict scrutiny cases? Griswold, Eisenstadt, and Lochner?
ANSWER: Due process decisions that seem to apply strict scrutiny, or something like strict scrutiny, would include Lochner, Pierce, Meyer, Griswold, Roe, Casey, Loving, Zablocki, arguably Lawrence, and Perry v. Schwarzenegger.