The electrical resistivity, p, of a metal is usually interpreted in terms of the mean free path (the average distance, l, an electron travels before it is scattered). As the temperature is raised, the resistivity increases and the apparent mean free path is correspondingly reduced. In this semi-classical picture, the mean free path cannot be much shorter than the distance, d, between two atoms. This has been confirmed for many systems and was considered to be a universal behaviour. Recently, some apparent exceptions were found, including alkali-doped fullerenes and high-temperature superconductors. However, there remains the possibility that these systems are in exotic states, with only a small fraction of the conduction electrons contributing to the conductivity; the mean free path would then have to be correspondingly larger to explain the observed resistivity. Here we report a model calculation of electron conduction in alkali-doped fullerenes, in which the electrons are scattered by intramolecular vibrations. The resistivity at large temperatures implies l << d, demonstrating that there is no fundamental principle requiring l > or = d. At high temperatures, the semi-classical picture breaks down, and the electrons cannot be described as quasiparticles.