Recently, the common methodology used to transform type Ia supernovae (SNe Ia) into genuine standard candles has been suffering criticism. Indeed, it assumes a par- ticular cosmological model (namely the flat LambdaCDM) to calibrate the standardisation corrections parameters, i.e. the dependency of the supernova peak absolute magnitude on its colour, post-maximum decline rate and host galaxy mass. As a result, this as- sumption could make the data compliant to the assumed cosmology and thus nullify all works previously conducted on model comparison. In this work, we verify the viability of these hypotheses by developing a cosmology-independent approach to standardise SNe Ia data from the recent JLA compilation. Our resulting corrections turn out to be very close to the LambdaCDM-based corrections. Therefore, even if a LambdaCDM-based calibra- tion is questionable from a theoretical point of view, the potential compliance of SNe Ia data does not happen in practice for the JLA compilation. Previous works of model comparison based on these data do not have to be called into question. However, as this cosmology-independent standardisation method has the same degree of complex- ity than the model-dependent one, it is worth using it in future works, especially if smaller samples are considered, such as the superluminous type Ic supernovae.