Since I am from the PE industry, I felt I have to say something.

1) PE is a small industry in Singapore, and the people hiring are mainly the banks, family funds, government funds (like GIC, Temasek) and a few institutions. I am excluding the funds of funds from this. By 'small' I mean the number of prospective employers and not necessarily the fund size they are managing.
2) story of Army Captain making the switch to PE directly does seem implausible as I definitely would not hire someone straight from the Army. Unless of course, he joins his family fund or he took an MBA from Harvard and had some internship before making the switch. Even so, at best he joins as an associate.

back on the topic on making transition to private sector. I worked in a statutory board for 5 years but managed to switch to an investment related role under one of the government holdings for another 5 years. In between, I took 2 years off to do an MBA in Stanford before joining the private sector in the PE industry. First based in HK and now in China.

I hope that helps.