Argument after the fact. What I mean is if you are willing to believe that an asari scientist is an adept in biotics then a politician is not different.
Liara did mention in ME3 that asari education includes biotic training - but since she'd also mentioned (in ME1) that not all asari really develop their biotics, I assumed that whatever training was required in school was basic control, e.g., learn enough control to not poke holes in the walls.
Liara apparently developed hers enough to protect herself when she went out on digs, yet she cowered in fear while Shepard & Co. fought the krogan battlemaster and his geth buddies. Perhaps she was much more comfortable with defense than offense at that time. Regardless, she panicked in that situation.
I always role-played / headcanoned that Ashley got Liara & Tali zeegee certified on a primary weapon and Kaidan worked with them in the use of biotic and tech skills in combat once I brought them aboard the Normandy.