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. In particular, no fine-tuning in the early Universe is needed, neither in general nor in order to explain the fact that no strong departure from flatness is observed today. 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 timescale. However, it is sometimes claimed 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 these arguments also do not imply that fine-tuning of the basic cosmological parameters is necessary and discuss some pitfalls of the typical Gedankenexperiment involved.