You need to take the entire statement in context, not just bits and pieces. You don’t loose your “temporary resident status”....it says nothing about a study permit.  The word “may” carries significant weight. It doesn’t mean you definitely will (or won’t for that matter) be allowed to apply for a study permit. You may be able to do a short term (less than 6 month) course or apply for a study permit. In applying as a refugee claimant, there is nothing to guarantee you will recieve that permit.
Persons making a claim for refugee protection in Canada with an existing temporary resident status do not lose their existing status. These persons 
may therefore attend a 
short-
term course of study without a permit so long as they complete the course within the period of their authorized stay.
Their existing status 
may allow for an in-Canada study permit application if, for example, they hold a work permit [
R215(1)(c)]. If they lose their temporary resident status (see 
A47 for loss of temporary resident status), they 
May apply for a study permit.