"History supplied evidence."

No

History itself does not supply evidence.

Historical evidence comes from sources such as documents, inscriptions, archaeological remains, artifacts, official records, and other traces of the past.

History, as a discipline, interprets those sources.

historians use historical evidence,

rather than

history supplies evidence.

Cherry-picking is a genuine methodological concern. Historians try to reduce it by comparing multiple independent sources, considering contrary evidence, and making their reasoning transparent. Whether a particular historian succeeds is open to critical evaluation.