I'll guarantee you that when you flex the stays apart by hand, each side is not moving the same amount off of center. In fact, you're probably moving one side 4mm and the other side none. So with the wheel in the frame, you've just misaligned the rear triangle by 4mm. Or maybe 3mm. Or maybe 2.5mm. Who knows.

The advantage to cold setting from 126 to 130 is that, if done right, you can have a frame that's properly aligned at the wider spacing. With some frames you can even end up with better alignment than you started with.

And any good bike shop can make sure the dropouts are aligned properly, and correct it if not, and can check derailleur hanger alignment and correct that, too.

If it's worth doing, it's worth doing right. And I'll add that if someone is changing the frame spacing to run a modern 10 speed cassette with indexed shifting, for example, the derailleur hanger alignment is critical.