OK, there are two (roughly) issues here. One is whether the frequency response is accurate, which (if it isn't) will throw off the SPL figure that is integrated over all frequencies. The other is the degree of accuracy to which the measurement software knows how SPL is converted into the numeric (internal) level that it actually reads. You can't get +/- 1 dB unless the specific microphone has been calibrated against a known reference. Even if the software knows the average of some particular microphone model (or phone etc), it doesn't know the figure for your exact microphone.