Those houses you quoted are usually NOT meant for locals, but rent out to expatriates with handsome housing packages, e.g. the family of a CEO or MD in a multinational corporation's regional headquarters in Singapore. Owners are looking for company lease only
I am surprised that these agents put an asking price there. The practice is to leave it blank or have an indicative range there. So when the HR person or agent representing the company call, the owner's agent will ask, "What's the company's budget?" And the maximum housing budget of the expatriate will be the asking rent.
If you work in an MNC, or you yourself (or you know someone) who rent/lease these houses, you'll know exactly what I mean