Severe depression/anxiety can't be treated with CBT Is there any evidence that supports the idea that a severe depression/anxiety can't be treated with CBT? 

Since, it's in severe state, and one has to use anti-depressants to lower the level, and then obviously CBT can help reduce a moderate to low level depression. Is a severe depression/anxiety too strong to be healed by CBT, and it makes the usage of anti-depressants necessary?
Yes, that is the consensus view among psychiatrists and clinical psychologists (e.g., Parker et al., 2012). A commonly referenced authoritative guideline for treatment of major depressive disorder is the NICE guide.  

Reference
Parker et al., Acta Psychiatr Scand (2013); 128(4): 271-81