A lefty myself, I can also throw right-handed, but not as well. I bat and swing a golf club lefty, but write, play tennis, and eat right-handed. I can write left-handed but, weirdly, find it easier to write right-to-left, mirror image style, than proper left-to-write when I do. Table tennis I have no preference, am equally bad from both sides, though.
I wouldn't say I'm ambidextrous -- I can kick a point after left-footed, but fell, twisting my ankle in the process, when I tried right-footed, and I can't write left-handed going left-to-right without getting some of the letter backwards. I self-identify as a lefty because I consider throwing a baseball the skill that defines one's handedness. But, it's actually more like nothing comes easy for me from either side. For example, my handwriting is terrible, all but illegible even to myself unless I really concentrate on it. Although, I draw tolerably well right-handed.
I wonder sometimes if it's related to the dyslexia my dad and youngest brother struggle with and my son's apraxia. In any event, Pat Venditte's achievement is remarkable.
I'm no fan of the A's, but I'll wish Venditte well whenever he's not facing the Red Sox.
And, yes, umpires needed new rules to deal with him.