Information about law in Syria is virtually impossible to find, but there is some evidence to support the claim. This article notes that exit stamps are required from the Damascus airport, that men between 18 and 24 are not allowed to travel without government permission. Information from US State Dept. indicates that "Syria charges a departure tax at its land and sea borders for all visitors except those on diplomatic passports and children under the age of 11". This page cites two articles indicating that Syria requires exit visa, based on "How Syria controls its dissidents - Banning travel". The Economist. 30 September 2010 and Ghadry, Farid N. (Winter 2005). "Syrian Reform: What Lies Beneath". The Middle East Quarterly. The Syrian Constitution allows for restricting exit in Article 38(3):
Every citizen shall have the right to move in or leave the territory of the state, unless prevented by a decision from the competent court or the public prosecution office or in accordance with the laws of public health and safety
There are individual travel bans,. Louay Hussein, who opposes the current regime, had to escape without permission. So the individual in question may have also said something negative about the government.