How do we ever know if our values are our own until we look back on them with hindsight?

Exactly this. People who do not reflect, who are not very self-aware, simply mirror the things that excite them or otherwise pull on their more exciting emotions (fear, anger, lust, et cetera). People on TV speaking loudly in angry tones of voice about fearful things excite them and draw their attention in ways they don't realize; and once they've decided something is fact (because the loud, angry talking head said it was) they don't want to re-examine it so much as they want to reinforce it.