Just because an OB is Western does not mean they will be pro-natural births. In fact I am not aware of any OB's at Gleneagles who would meet that criteria although I am happy to be corrected of anyone knows otherwise !
If you want a low intervention birth then you'd be better off looking for an OB who meets that need first of all - most OB's can practise at any hospital. Having said that, the way that the nurses work will make a big difference to your birth since they will be the ones who actually care for you during your labour - and as far as I am aware Gleneagles is not generally known as a low intevention hospital. NUH or Thomson Medical Centre would be, depending on which OB you have.
I'm not aware of the standard of care varying according to whether you are insured or not. But they will tend to assume that western expats (if indeed that is what you are!) are insured up to the hilt - so if you are paying for it yourself, watch out as they charge for everything ! And I mean everything - fetal monitoring, pads, lates gloves, dressings, use of the shower, they even charge you for doing vaginal exams ! Worth checking over the bill very closely before you pay it.