Actually, this is not completely accurate (we moved to Phils from BKK a few months ago). Bank rules vary slightly, but its pretty universal that you do have to be a resident and in fact they will ask for the ACR (residence card) and lease agreement. In fact, even Filipinos must have a valid written lease agreement or proof of home ownership, which is part of the reason a very large proportion of Filipinos are unbanked (cash is still king here).
We spoke to several banks and I have never heard of 3-yr rule, although its possible it exists at a bank I never spoke with.
In the end, I decided to not bother with getting accounts in my name -- my wife is a Filipina, so eventually (after securing apartment lease, etc.) we were able to open accounts in her name. I still can't open an account as I have no intention to get the ACR card since I can get a 12-month stamp at entry as long as I arrive with her -- very easy and puts the Thailand spouse visa (or any other visa) to shame.
Bottom line, if you close the account it will be impossible to open a new one without moving here and officially stablishing residency