How Can Others See Trips I Can't? 

This depends on how the requestors are issuing trips.

Most are sent to the driver pool in a ‘wave’. The computer randomly selects names and sends it to the App until the trip fills. If directly assigned due to needing hard plates, driver’s DL status, DOT cards, TWIC cards, CDL drivers, personal chase and other determining factors can mean that only certain selected drivers will see those trips. There are also FCFS (First Come, First Served) trips that will appear for anyone within the start radius.