Bill (Grannyring), you have not misunderstood what has been said. If your state charges sales tax for in-state purchases, its residents are almost certainly also liable for use tax on out-of-state purchases of items and services that would be subject to the tax if purchased in-state. See the second page of the link I provided earlier. As rcprince mentioned, however, enforcement of those laws by the states is certainly problematical for them.
In the case of Amazon specifically, their presence in many states requires them to collect sales tax for sales to residents of those states (consistent with Dave’s comment above). And I believe that the huge scale of their operations has prompted some states to try (successfully in some cases) to get them to collect sales taxes in some states they don’t have a presence in.
I have no knowledge of Turbo Tax, as I don’t use it or anything similar, but in my state (Connecticut) the income tax form includes a line item and an associated worksheet for computation and reporting of the use tax that is due. If one knowingly makes a false entry on that line, perhaps such as zero, one is signing a fraudulent return.
Also, the state has in the past published online the names of particularly notorious use tax scofflaws it has identified and pursued.
Best regards,
-- Al
