Perfidy's prefix

[bmo]

Per-, American Heritage Dictionary and www.etymonline.com give two different explanations for this prefix, destruction and through, respectively. I am having a hard time trying to consolidate. What do you think? Thanks a lot.

 

[Casiopea]

From American Heritage,

ENTRY: per1
DEFINITION: Base of prepositions and preverbs with the basic meanings of “forward,” “through,” ...


From Online Etymology Dictionary,

per (preposition) 1588 (earlier in various L. and Fr. phrases), from L. per "through, ...

perfidy from L. perfidia "falsehood, treachery," from perfidus "faithless," from phrase per fidem decipere "to deceive through trustingness," from per "through" (see per) + fidem, acc. of fides "faith" (see faith).