The FMCSA has indicated that roadside manuals for ELDs are required to be kept with the driver at all times. This rule was amended by the FMCSA under the "Regulatory Guidance Concerning Electronic Signatures and Documents” (76 FR 411) publication allowing for the roadside manual to be in electronic format for drivers during roadside inspection.
If an inspection officer tells you that a physical copy is required to be compliant he is misinformed and you should direct him to the link below. In this link from FMCSA there is a response under Question #5 that states: