This is a limitation on the data, but it's not the main criticism of Fryer.
The principle issue is that Fryer controls for the rate of interactions with the police, but that rate is effectively determined entirely by police officers (who have wide discretion in who to stop/pull over) and departmental policy (i.e. how many patrols get assigned to which neighborhoods). This means that we've already prevented ourselves from considering one major avenue where we have very solid evidence that racial bias is introduced, and, in particular, it means that the group "white people stopped by the police" is not identical to the group "black people stopped by the police:" black folks are substantially less likely to be engaged in criminal activity when they interact with the police. This article covers some of the methodological issues pretty well; if you're pressed for time you can scroll down to the infographic, which helps visualize some of the difficulty in this kind of analysis.
But the short version is this -- if the police are stopping more 'innocent' black folks (i.e. people with no contraband, weapons, or outstanding warrants on them at the time), but they're still being killed at a roughly equal rate to whites, this doesn't demonstrate an absence of bias at all. Quite to the contrary, it suggests that there is racial bias at play: there appears to be a lower threshold for killing black suspects than white ones.
As an analogy, imagine you're testing a new medication to prevent breast cancer, and you let doctors just recruit people for the study that they think could benefit from it. The doctors recommend that most of their female patients join their study, because breast cancer is a common problem for women, but they only recruit a handful of men who show some additional risk factor (e.g. a particular genetic marker). At the end of the study, you find that 0.1% of people who take the medication develop breast cancer within one year. Upon further examination of the data, you realize that this number is true across all groups: i.e. 0.1% of men who take the medication develop breast cancer, and 0.1% of women who take the medication develop breast cancer. Would you say that this medication is equally dangerous for all groups? If so, you're missing the fact that these two groups didn't have equal risks for breast cancer to begin with -- the drug could actually be lowering the risk for one group, while raising it for the other.