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I think that's one of the exceptions to the octet rule. He was referring to that fact that Boron is stable with only 6 valence electrons, and therefore only shares three bonds with fluoride in BF3 and has no lone pairs (a lone pair would complete the octet rule, if it applied to Boron).
Boron is in group 13 along with Aluminum. They both need 5e- to complete their octet and are apart of a class of Acid-Base reactions. Boron in BF3 only completes its octet if another atom provides both e- to form a coordinate covalent bond.
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