My suspicion is that the Collector app for iOS (and maybe Android, too; I don't have one) uses a stationary speed filter when it acquires coordinates to prevent measurements from jumping around when the unit is stationary.
I tried this out in the field using a points feature class based map. I put my iPhone 4S on a monumented location and let it settle for a minute. The location icon changes from a bearing (motion) arrow indicator to a solid blue circle indicating lack of movement. If I collect a series of measurements without moving the phone, the readings all have the exact same coordinates (not very likely based on the inherent repeatibility of GPS). This, I think, is because since the phone hasn't changed location within X meters (whatever is coded in the app), the app considers it stationary and uses the last set of coordinates acquired.
If I collect a measurement on a monumented location, and then move off of it about 10 meters (the location icon shows movement) and then return the phone to the monumented location, let it settle until the stationary icon appears, and collect another measurement, the coordinates are different (like you'd expect).
While I can see the practical aspect of such an arrangement, it makes it difficult to determine the inherent precision and/or accuracy of the system.
Comments?