This question is correct, in the sense that if you truly never wish to take any kind of debt, you do not need to care about your credit score. I will assume a rational person who doesn't generally need loans and managed finance well.

The flaw however is it may be infeasible for many people in the modern world to live without any kind of debt at all. Some common transactions technically involve debt, some obvious and some less obvious follow (note this may vary between countries and states):

• Getting a mortgage
  • This is a fairly obvious example of a time some people consider debt justified, to buy a primary home, which for many people is infeasible to do outright in cash
  • You can validly argue that one could instead rent until they have the money to buy a home in cash, however that brings my next point
• Rent an apartment
  • Many, if not most landlords will run a credit check before allowing one to rent an appointment, this is in part because you could potentially damage the apartment beyond the value of the deposit and they want to know you are good to pay if so
  • They may also use this to judge your general responsibility and reputation, to find customers who they feel are low risk of problems, or defaulting on their rent, as in essence given it takes time to evict someone, they may end up in a situation where you owe them for rent, credit is then important
• Rent a car
  • The reasons for this are basically the same as above, having a valuable asset that doesn't belong to you and risk of default, however many would not consider this to relate to credit at all
  • Some companies may refuse you all together without good credit, others will want a greatly enlarged deposit of funds
• Post pay utility bills
  • If you want to pay your utilities at the end of the month rather than being required to prepay, or use a meter which requires buying credit in advance you are also essentially taking credit
  • Depending on the utility company they may run a credit check for this
• Cell phone plan (also applies to landlines)
  • If you use a contract cell phone as opposed to a PAYG one, you will likely need a credit check, both to check if you are likely to pay your bill and if you could pay for the phone if it were damaged or lost
  • This is a relatively avoidable situation as many prepay phone plans exist
• Internet or TV service
  • Many ISPs and TV service providers want to check credit both to know if you will pay your bills and if they loan equipment to you if you are likely to be able to pay for it
• Credit cards
  • While avoidable these still offer perks, particularly in better cards which will require a high credit score
  • They offer greatly improved fraud protection over cash, check or debit card, with lower customer liabilities and lesser consequences to you
  • They often offer rewards and cash back, which while not worth it if you might fall into debt and negate this benefit with fees, do give you free money if you can pay in full and on time reliably
• Car (and other) insurance
  • While not a form of credit many insurance companies use your credit score to decide how reliable and financially stable you are
  • If you have poor credit they may refuse to insure you or offer punishingly high rates
  • This is illegal in some jurisdictions so may or may not be a problem

So in summary, yes, if you do nothing that involves any kind of debt, even subtle or indirect debt you do not need to care about your credit score at all, otherwise it may be important for activities you may wish to do (the list above is incomplete, there are many other such cases, and some of these only apply in some places).