We consider reliable telemetry in white spaces in the form of protecting the integrity of distributed spectrum measurements against coordinated misreporting attacks. Our focus is on the case where a subset of the sensors can be remotely attested. We propose a practical framework for using statistical sequential estimation coupled with machine learning classifiers to deter attacks and achieve quantifiably precise outcome. We provide an application-oriented case study in the context of spectrum measurements in the white spaces. The study includes a cost analysis for remote attestation, as well as an evaluation using real transmitter and terrain data from the FCC and NASA for Southwest Pennsylvania. The results show that with as low as 15% penetration of attestation-capable nodes, more than 94% of the attempts from omniscient attackers can be thwarted.