1 Job + 1 Job = No Job

Did you catch this story about the Revenue Canada lawyer in Toronto who accepted a second job in Ottawa without telling either employer that she had another job.   She claimed she was trying out the Ottawa job to see if she wanted to take it full time and quit the Toronto job.  To hide the Ottawa job from her Toronto employer, she took vacation time and then called in sick and apparently submitted doctors’ letters (which were obviously not accurate).   When the employers found out what was going on, they both fired her.  She then filed a grievance against the Toronto employer, which was dismissed by a federal adjudicator.  
Lying to your employer about reasons for absence is obviously serious dishonesty.   What if this woman had simply used her vacation time from the Toronto job to try out the Ottawa job for a couple of weeks (and not falsely called in sick)?  Would the Toronto employer have had grounds for dismissal then?