All you'll probably become after three weeks in the US is a child of the magenta line !
I'm wondering if the above quoted qualification is really based on aviation experience.
Fact is, there is a minimum number of hours required to earn a pilot certificate (e.g. 45 hours for PPL). How long it takes to attain a pilot certificate depends on individual ability (knowledge, skills, mental readiness) and, of course, flying frequency. Obtaining a PPL status within 21 days, for example, is advantageous and beneficial (e.g. if time constraints is a factor), as long as the training ensures that the aviation procedures are accomplished with structure, accountability and substantial information quality.
Where you do the training (US or Europe) is totally irrelevant in terms of becoming a safe and competent pilot. Training in Arizona under favorable charlie weather conditions or in the UK where mostly delta/mike conditions prevail is structured with the same goal, to make you become a safe and competent pilot.
I did my JAR training (based on CAA rules and regulations) in the US (flying under FAA regulations) and it made me competent to fly in both US and Europe airspace and jurisdictions.
The key is to understand your needs and map out the training landscape accordingly to suit those needs and you should be able to successfully manage your training to attain a pilot certificate.
WP