Yes, I've learned that the hard way. Provided they give you payment in lieu of notice, they don't need much of a reason to let you go.
Myself and a co-worker were once let go for "performance reasons" at 10 months - just after project completion (successful). It was beyond my probationary period, and no issues where raised in the 2 performance reviews.
Their notice period was just 1 month. We were effectively cheap contractors.
My advice now is to treat offers with a low notice period (of them telling you) as a red flag. The norm is 3 months, after probation.
