It seem to me there's some confusion between what is client side and what is server side.
When Beas pushed the button on the phone (the client) the phone begins initiating the process of trying to send the information. The phone must then establish a connection with Facebook (the server) through the cell phone company's towers. This can take anywhere from milliseconds to hours depending on the circumstances. When Facebook finally receives the message, it process the message, posts it, and puts a time stamp on it (the time shown on the Facebook post).
It is key to note that this time may not indicate the time of the button press. How well the two times correlate to one another can be determined through a statistical study (information that may or may not be available). This information will only tell the probabaility of Beas pushing the button within an interval of time (however long is determined to have an effect on her driving). Beas' button press may also be a statistical outlier and not fall into the interval of time being looked at.
However, if Beas' cell phone keeps timestamp of when the button was pressed (client side), then we just look at that and forget everything else.
