The invisibility is a rule, not a courtesy, and the pair of provisions is worth reading together. 15 USC 1681b(c)(3) provides that "except as provided in section 1681g(a)(5) of this title, a consumer reporting agency shall not furnish to any person a record of inquiries in connection with a credit or insurance transaction that is not initiated by a consumer." The exception it points to is the consumer's own disclosure right: 15 USC 1681g(a)(5) requires the agency to disclose to you "a record of all inquiries received by the agency during the 1-year period preceding the request that identified the consumer in connection with a credit or insurance transaction that was not initiated by the consumer."
Read together, those two sentences produce something unusual in consumer finance: a category of information Congress made visible to you and invisible to everyone else. It is also why the commercial description and the legal one line up so neatly. Fair Isaac's "not visible to lenders" is a statement about the market; 1681b(c)(3) is the reason.
What actually produces a soft inquiry. Four families cover almost all of them.
Your own request. Fair Isaac states that "checking your credit report won't affect your FICO Scores, as long as you order your credit report directly from the credit reporting agency or through an organization authorized to provide credit reports to consumers." The qualification is doing real work: it is the route that matters, not the act of looking.
An existing creditor's account review. 15 USC 1681b(a)(3)(A) permits furnishing a report in connection with "the extension of credit to, or review or collection of an account of, the consumer," and (a)(3)(F)(ii) permits it where a person has a legitimate business need "to review an account to determine whether the consumer continues to meet the terms of the account." This is the case that breaks the tidy "you asked for it" framing, because a periodic review of a card you already hold is neither an application nor something you initiated.
A prescreened firm offer. Under 15 USC 1681b(c)(1)(B) a bureau may furnish a report for a credit or insurance transaction you did not initiate where the transaction "consists of a firm offer of credit or insurance," the agency has complied with the opt-out machinery, and you have not elected out. The limit on what the sender receives is narrower than most people assume. Under 1681b(c)(2) the recipient may receive only your name and address, "an identifier that is not unique to the consumer and that is used by the person solely for the purpose of verifying the identity of the consumer," and other information that "does not identify the relationship or experience of the consumer with respect to a particular creditor or other entity." So a preapproved mail offer does not hand the sender your accounts or your balances.
Employment and insurance screening. These carry their own rules, including the standalone written disclosure and authorization an employer must obtain, and they are disclosed to you for a longer period: 15 USC 1681g(a)(3)(A) requires identification of each person who procured a report for employment purposes during the preceding two years, against one year for any other purpose. Note that an employment inquiry sits outside 1681b(c)(3)'s furnishing bar altogether and is still treated as soft, which is the second reason the trade terms and the statute cannot simply be merged.
The lever, and its two tiers. If the prescreened offers are unwelcome, 15 USC 1681b(e) gives you an election to have your name and address excluded from the lists furnished for firm offers. The mechanics reward reading, because the two routes are not equivalent. Under (e)(2) you may notify the agency either through the notification system it is required to maintain, including a toll-free telephone number, or by submitting a signed notice of election form the agency issues. Under (e)(4) the election takes effect five business days after notification, and then the durations diverge: notification through the telephone system alone lasts for the five-year period beginning five business days after you called, while an election made on the signed form lasts "until the consumer notifies the agency" that it is no longer effective. The election also applies to each affiliate of the agency.
On the score effect, state it as the vendors state it. "It does not hurt your score" delivered flatly is a claim about a model nobody outside the vendor can inspect. Fair Isaac's own wording is available and is enough: soft inquiries such as viewing your own report "will not affect your FICO Scores." The categories above describe how these requests are treated in practice, which is a different thing from a classification either model developer sets out in full.