Unless you live in a very small community, giving your word isn't as binding as it once was. Thieves and swindlers have long defrauded insurance companies. The costs of their antics are reflected by increased costs for those who are honest. When you're getting car insurance quotes, your insurance company will usually take your word when you describe your car's condition. Unless you own a very valuable collector's car, an in-person inspection isn't usually required. If you buy your insurance from a local agent, they might check your car if they're nearby or at your home closing the deal. Any preexisting damage, like a dented fender or cracked windshield, will be noted, so it would be excluded in the event of a claim.
If you file a claim for a collision, your insurance company might require a police report. The report will detail the damage and cite the facts. Outside of that, the insurance company will send a claims adjuster to check your vehicle to see how badly it was damaged and the extent of the repairs needed.
If it is determined that your car would cost more to repair than it is worth on the open market, your insurance adjuster will declare it totaled and you will receive adequate compensation for its value. If it can be repaired, the adjuster will note what damage was caused in the collision and what might be preexisting damage.
Before showing up for the inspection, it's likely the adjuster will check the vehicle's history to see if it had ever been totaled or sold as junk. Any re-titling or "title washing" can be spotted by a good adjuster. Junk cars can be good investments for mechanics but not for insurance companies.
During the adjuster's hands-on inspection, the areas of obvious damage will be closely checked. Rust, sanding, and mismatched paint are all signs of old repairs and damage. As long as you're not trying to get a repair made for damage that happened last year, you'll have no problem passing the adjuster's exam.
Your adjuster will also look for other signs that a car had a dark history, like mismatched upholstery or electrical system frailties, such as those found on cars that were submerged in flood water. A person who inadvertently bought a flood vehicle may be trying to pass along their loss by faking a collision.
Adjusters are well trained to determine which damage on a vehicle is new or old. They're as savvy as the detectives on television. In fact, they are detectives, trying to determine how much to pay to fix your car after an accident. They are not out to cheat you. Remember this when getting car insurance quotes.