We reconsider the impact of ν¯e↔ν¯μ,τ neutrino oscillations on the observed ν¯e signal of supernova SN 1987A. Performing a maximum-likelihood analysis using as fit parameters the released binding energy $\Eb$ and the average neutrino energy $\Ee$, we find as previous analyses that ν¯e↔ν¯μ,τ oscillations with large mixing angles have lower best-fit values for $\Ee$ than small-mixing angle (SMA) oscillations. Moreover, the inferred value of $\Ee$ is already in the SMA case lower than those found in simulations. This apparent conflict has been interpreted as evidence against the large mixing oscillation solutions to the solar neutrino problem. In order to quantify the degree to which the experimental data favour the SMA over the large mixing solutions we use their likelihood ratios as well as a Kolmogorov-Smirnov test. We find within the range of SN parameters predicted by simulations regions in which the LMA-MSW solution is either only marginally disfavoured or favoured compared to the SMA-MSW solution. We conclude therefore that the LMA-MSW solution is not in conflict with the current understanding of SN physics. In contrast, the vacuum oscillation and the LOW solutions to the solar neutrino problem can be excluded at the 4σ level for most of the SN parameter ranges found in simulations. Only a marginal region with low values of $\Ee$, <Eν¯μ,τ> and $\Eb$ is left over, in which these oscillation solutions can be reconciled with the neutrino signal of SN 1987A.