It can be a problem in the US as well. AFAIK, most states now require the mileage to be documented on the registration application, including renewals. That means, the state has a record of the reported mileage for each year the registration was renewed. Now, I don’t think they actually verify the mileage, but if one is going to lie about it, you would have to at least be consistent about it. Most dealers will record the mileage when they service the vehicle. I am pretty sure independent shops also record the mileage, but that may not be universal. Now, you would have to know what shops the previous owner used for service, and probably have the previous owner agree to let you see the service records, but if they won’t agree to that, it would be a big red flag.
Interesting that you mention specifically BMW E39s and E46s. as these were some of the first cars that, again AFAIK, stored the mileage both in the car’s computer as well as the instrument cluster, and if they did not agree they would display an error. The programming was, in fact, was sophisticated enough so that if you replaced the instrument cluster with a new one, the car’s computer would recognize the zero value in the new cluster and replace it with the value stored in the computer. It was a pretty bullet-proof system, but about 10 years ago, someone posted a procedure that, if you could get a copy of the BMW software, you could change the value in the car’s computer. Now, the procedure is fairly complex and if you did it incorrectly, you would “brick it”, that is, make the computer about as useful as a brick. Not something a backyard mechanic would attempt, but a competent mechanic working for a shady used-car salesman could probably be successful with it.
Another thing that is common in the US is that if the age of the vehicle is over 10 years, the registration requirement for reporting mileage is often optional and they will accept a value of “UNKNOWN” for title purposes. The last car I titled had the mileage on the title, but it also had the disclaimer that because of the age, the mileage reported may not be accurate.
The only thing a buyer can do is either buy from the original owner and review the service records. If that is not possible, assume the mileage may or may be accurate and base you decision on that fact.