Does the saying qui tacet consentire videtur (silence implies consent) carry any weight in civil litigation?
For example, suppose that Alice emails Bob, "When I began work we agreed that the rate was $100/hour." Another email from Alice to Bob says, "I worked all weekend to fix that!" Years later these emails are admitted as evidence in civil litigation pertaining to money owed for work Alice did for Bob. Bob testifies that he did not agree with either assertion, but he can't produce any contemporaneous objection (e.g., a reply Email saying, "I disagree.")
Can a trier of fact (judge or jury) consider the lack of a contemporaneous objection as evidence of contemporaneous consent? Is there any law suggesting that such an inference should or should not be made?
(Interested in common law jurisdictions; U.S. in particular.)