Several authors have made claims, none of which has been rebutted, that the flatness problem, as formulated by Dicke and Peebles, is not really a problem but rather a misunderstanding. Nevertheless, the flatness problem is still widely perceived to be real. Most of the arguments against the idea of a flatness problem are based on the change with time of the density parameter Ω and normalized cosmological constant λ and, since the Hubble constant H is not considered, are independent of time-scale. An independent claim is that fine-tuning is required in order to produce a Universe which neither collapsed after a short time nor expanded so quickly that no structure formation could take place. I show that this claim does not imply that fine-tuning of the basic cosmological parameters is necessary, in part for similar reasons as in the more restricted flatness problem and in part due to an incorrect application of the idea of perturbing the early Universe in a gedankenexperiment; I discuss some typical pitfalls of the latter.