@Adam ********
As I said before, but you have missed that obviously, "you NORMALLY", so some countries might have other procedures for this.
When you say flatly false, maybe you should give an example of a country that has a different procedure, and describe that procedure.
Maybe when I show the official text from your home country about this:
Report your Visa Lost/Stolen to the U.S. Embassy or Consulate Abroad
To report your visa lost or stolen, email the Consular Section at the U.S. Embassy or Consulate outside the United States which issued your visa. Go to the U.S. Embassy or Consulate website to locate the email address and contact information. Be sure to include your full name, date of birth, place of birth, address in the United States, and an e-mail address (if available). Specifically state whether the visa was lost or stolen. If you have a copy of the passport or visa, scan and email this to the embassy or consulate. Otherwise, if known, report the category of visa, and the passport number from the lost/stolen visa.
If you have already reported your visa lost/stolen to the U.S. Embassy or Consulate, and then you later find your misplaced visa, then your visa will be invalid for future travel to the United States. Therefore, in that situation you must apply for a new visa at the U.S. Embassy or Consulate.
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Most countries have about the same rules for this situation as it is the most safe and logical thing to do.