TBH I’m not 100% sure that I’d believe that, but maybe Singapore is different. In the UK, it’s certainly possible to get mobile (cellphone) SIMs with a public static IP. But to get one you typically have to go to a specialist data provider. The ordinary cellphone droids know very little about this service and so typically you get the answer that it can’t be done. As an example see:
http://www.nucleusnetworks.co.uk/mobile-broadband/3g-static-fixed-ip.htm
There’s some significant cost associated with this service - certainly it’s not as cheap as having a standard mobile dynamic address, but it’s not outrageously expensive either - you’re looking at maybe US$20-25 per month for a bandwidth allowance of 1-3GB.