The author hypothesises that a key driver for the change in behaviour is a belief by the employees that they will be challenged on what they are booking their time to. A possible solution to this is a third party online timesheet service that guarantees that employers cannot identify what time employees are booking their time to, but only provides data in aggregate. This anonymisation technique is already in use for surveys, and as such it should be possible to automate the anonymisation (i.e. not giving the employer granular data where this would enable identification of employees). The employer would still be able to check whether employees were filling in timesheets or not.
The system may not work for small organisations or for projects where only a few people work on them, and of course would need good security to gain the trust of the employees.