That is not true. Maybe your idea is nice, but in reality it only depends on the dates on your ticket. So you can arrive with your return date after 1 month (ticket), and with a 1 month health insurance. But the stamps in your passport will say 3 months.
"need to buy health insurance for the whole 3 months" From what I understand you need health insurance for the duration of your stay. It does not depend on your visa, but on the dates on your flight tickets. Which are ehhhh... Free to change, depending on the airline. So I can imagine that you fly back after 4 weeks. But once you are in Thailand you "change your mind".
I used that same link already 2 times in the past year and never had a problem. And if there was a problem you would not be the only one complaining... So it is most likely a problem with your bank.
Maybe you can ask for some visa extension even when knowing that they will deny it? I understood that you will get a 7 day stamp or so to leave the country? Maybe that is better than overstay?