In photoacoustic tomography (PAT) the image contrast is due to optical absorption, and because of this PAT images are sensitive to changes in blood oxygen saturation (sO2). However, this is not a linear relationship due to the presence of a non-uniform light fluence distribution. In this paper we systematically evaluate the conditions in which an approximate linear inversion scheme–which assumes the internal fluence distribution is unchanged when the absorption coefficient changes–can give accurate estimates of sO2. A numerical phantom of highly vascularised tissue is used to test this assumption. It is shown that using multiple wavelengths over a broad range of the near-infrared spectrum yields inaccurate estimates of oxygenation, while a careful selection of wavelengths in the 620-920nm range is likely to yield more accurate oxygenation values. We demonstrate that a 1D fluence correction obtained by fitting a linear function to the average decay rate in the image can further improve the estimates. However, opting to use these longer wavelengths involves sacrificing signal-to-noise ratio in the image, as the absorption of blood is low in this range. This results in an inherent trade-off between error in the sO2 estimates due to fluence variation and error due to noise. This study shows that the depth to which sO2 can be estimated accurately using a linear approximation is limited in vivo, even with idealised measurements, to at most 3mm. In practice, there will be even greater uncertainties affecting the estimates, e.g., due to bandlimited or partial-view acoustic detection.