Two failures, priced
When an assistant does not know something it can do one of two things. It can say so and point somewhere, or it can produce the closest plausible answer it can assemble from whatever material was nearest.
The first costs the visitor one extra step: they now have to email, call, or search. That step is annoying and it is bounded. They are exactly where they would have been if the assistant had not existed.
The second costs whatever the wrong answer causes. Someone drives across town to a shop that closed an hour earlier. Someone books an appointment for a service you do not offer. Someone buys the wrong size because the assistant paraphrased a sizing chart it could not really read. Someone believes a price that is a year out of date and arrives expecting to pay it. Each of these takes staff time to unpick, and the unpicking is done by a person, at a moment when the customer is already unhappy.
The wasted journey is the honest example
Pick the concrete case rather than the abstract one when you are arguing this internally. Opening hours are the cleanest.
A visitor asks whether you are open on a public holiday. The assistant does not have a holiday schedule, but it does have a page that says you are open seven days a week. Reading the two together, the plausible answer is yes. The person drives over, finds a closed door, and the cost of that is not one wasted trip. It is a customer who now believes your website lies, which they will mention to whoever they were meeting.
The refusal version of the same event is a sentence saying it does not have holiday hours and here is the number to call. The visitor is mildly irritated and phones. Nobody drives anywhere.
Trust is the part you cannot recover
The direct cost of a wrong answer is bounded by the incident. The indirect cost is not, because it applies retroactively to every correct answer the system ever gave and prospectively to every one it will.
A visitor who catches one confident falsehood has no way to tell which of the other answers were also wrong. They have no visibility into which questions were well covered by your material and which were reached for. From the outside, every answer arrives with identical confidence. So the rational response to one detected error is to distrust the channel entirely, and that is what people do.
This is why the trade is asymmetric rather than merely uneven. Refusals do not accumulate into a reputation. Wrong answers do. An assistant that refuses often is described as limited. An assistant that is wrong occasionally is described as unreliable, and unreliable is a much harder word to come back from.
Internally, wrong answers are also more expensive to handle
There is a second asymmetry that support leads feel before they can articulate it. A refusal generates a normal inbound contact: a person asking a question, arriving through your usual channel, which your team is set up to handle at the usual cost.
A wrong answer generates a correction. The customer arrives already holding a claim they believe came from you, and the conversation now starts with your agent contradicting something the company said. That takes longer, it needs a more senior person more often, and a meaningful share of the time it ends in a goodwill gesture rather than an explanation.
So the refusal is cheaper on both sides of the desk. It is only more expensive in the report, where it appears as a failure and the wrong answer appears as a success.
Where the threshold belongs
Most systems that answer from your own material expose some control over how close a match has to be before the system will attempt an answer. Askably makes this explicit: below the threshold you set, it returns a fallback you wrote rather than reaching for the model at all. Whatever the tool, the setting exists somewhere and it usually ships in the middle.
The useful way to set it is by consequence rather than by taste. Ask what the worst realistic wrong answer in your domain costs. If the worst case is a customer reading a slightly stale feature description, you can afford to be generous. If the worst case is somebody arriving at a locked door, taking the wrong medicine, missing a legal deadline, or bringing the wrong documents to an appointment, be strict, and accept a higher refusal rate as the price of that.
Do this per business, not per industry. Two shops selling the same thing can have very different worst cases depending on whether their customers travel to reach them.
A refusal is not the same as being useless
The reason refusals get a bad reputation is that most of them are written badly, which is a separate problem with a separate fix. A refusal that says sorry, I could not find that, and stops, has genuinely wasted the visitor's time.
A refusal that says what it cannot do, names the route that can, and offers to take a message has done real work. It has told the visitor the channel does not cover this, which is information, and it has moved them one step closer to an answer rather than leaving them to guess.
Judge your refusals by that standard rather than by their frequency. A high refusal rate with good wording is a working system with content gaps you can now see. A low refusal rate with unknown accuracy is a system you cannot evaluate at all.