Captain reported aircraft log book errors were discovered during an interview with the FAA for an occurrence report review.

Narrative

During an interview with an FAA representative concerning an Occurrence Report; the FAA representative indicated that the maintenance log may not have been properly filled out. Specifically; a box labeled 'P/R' was not checked.The interview was in reference to an event which occurred on Date1 wherein the flight crew performed an emergency descent and landing. The descent and landing was in response to an EICAS message: 'CABIN ALTITUDE HI'.For that incident; the following narrative was submitted in a Report on Date2: 'During climb to cruising altitude of FL310; (enroute from ZZZ to ZZZ1); the EICAS indicated 'CABIN ALTITUDE HI' at approximately FL 270. The Crew performed duties in accordance with the emergency procedures checklist and QRH. Flight deck crew Reported the warning to ATC; informed Dispatch and determined to land immediately at the nearest airport; ZZZ2. No-one was injured during the incident. Maintenance cleared the aircraft for service and the flight proceeded to the scheduled airport; ZZZ1.'This report is in response to to the possibility; indicated by Name (The FAA representative) that a box in the maintenance log may have been inadvertently left unchecked prior to the aircraft being returned to service for continuation to the originally planned destination; ZZZ1.I was asked if I had verified the maintenance log and noticed that the box was not checked. I responded that I verified the signature of the Maintenance representative. I also indicated that I did not recall if a box was left unchecked. However; I received and reviewed the Dispatch Release which indicated that Maintenance had cleared the aircraft to return to service.Name suggested that returning to ZZZ; was a viable option. I indicated that it was ATC who suggested that we divert to ZZZ2 as it was the closest airport. In fact; ZZZ2 was so close that I had a very short time to update the FMS with the new destination and set the landing conditions. The FO (First Officer) tried to assist with the FMS entries and I found it necessary to remind him that his primary duties were to fly the aircraft; and that standard operating procedures prescribed that the Pilot Monitoring; myself; to set up the FMS.I will discuss this with the training department and the maintenance department and make a habit of asking maintenance representatives to double-check for completion of the maintenance log.