reading/writing flatfiles with simultaneous users?

I have a script that takes in variables from the user (user name, ipaddress, refering page, etc) and writes them to a file. This file is later read by another script to produce various stats. My question is, does php only let one instance of a script execution open and read a flatfile at a time? Obviously a flatfile has severe design limitations compared to a database, but can it be kept accurate enough with proper programming methods? - Craiger