One possible answer is that the letter is basically authentic but has been interpolated.But, instead of that, we find that even inquiry in regard to our case is forbidden. For the younger Pliny, when he was ruler of a province, having condemned some Christians to death, and driven some from their steadfastness, being still annoyed by their great numbers, at last sought the advice of Trajan, the reigning emperor, as to what he was to do with the rest, explaining to his master that, except an obstinate disinclination to offer sacrifices, he found in the religious services nothing but meetings at early morning for singing hymns to Christ and God, and sealing home their way of life by a united pledge to be faithful to their religion, forbidding murder, adultery, dishonesty, and other crimes. Upon this Trajan wrote back that Christians were by no means to be sought after; but if they were brought before him, they should be punished.
A version of this has already been suggested by Herrmann. The basic idea is that section 9-10 is a later addition.
This passage a/ seems to shift from the problem of anonymous allegation of Christianity to the problems caused by a mass Christian rural movement, b/ is probably not referred to by Tertullian, c/ is not referred to by Trajan in his reply to PlinyI therefore postponed the investigation and hastened to consult you. For the matter seemed to me to warrant consulting you, especially because of the number involved. For many persons of every age, every rank, and also of both sexes are and will be endangered. For the contagion of this superstition has spread not only to the cities but also to the villages and farms. But it seems possible to check and cure it. It is certainly quite clear that the temples, which had been almost deserted, have begun to be frequented, that the established religious rites, long neglected, are being resumed, and that from everywhere sacrificial animals are coming, for which until now very few purchasers could be found. Hence it is easy to imagine what a multitude of people can be reformed if an opportunity for repentance is afforded.
Whether removing section 9-10 would reduce the stylometric issues with the letter is unknown AFAIK but it would be interesting to find out.You observed proper procedure, my dear Pliny, in sifting the cases of those who had been denounced to you as Christians. For it is not possible to lay down any general rule to serve as a kind of fixed standard. They are not to be sought out; if they are denounced and proved guilty, they are to be punished, with this reservation, that whoever denies that he is a Christian and really proves it--that is, by worshiping our gods--even though he was under suspicion in the past, shall obtain pardon through repentance. But anonymously posted accusations ought to have no place in any prosecution. For this is both a dangerous kind of precedent and out of keeping with the spirit of our age.