The loop area of your probe is acting as a nice antenna for the switching noise radiating off of the power supply and the common-mode noise currents flowing on the output cables. The common-mode noise currents cause a changing magnetic field in the vicinity of your power supply, which in turn get converted to a differential mode voltage that shows up on your oscilloscope input.
When power supply manufacturers measure ripple, usually they use a "ripple probe", that is a probe with a very small enclosed loop area loop area. The best way to do this is to use a probe tip BNC socket which allows you to plug the oscilloscope probe directly into a coaxial connector which is then wired to the power supply output. Manufacturers typically also specify a small capacitance at the end of the cable (10uF-100uF + 0.1uF ceramic). Most power supply manufacturers also use a 20MHz bandwidth limit on the oscilloscope. To further reduce EMI pickup, make sure to use a 1x probe.
With this setup, you have a more realistic idea about the power supply's actual ripple. Of course, even with the "real" ripple of the power supply, near-field radiated emissions can still cause system problems. As you saw with your accidental antenna probe, it can be quite easy to pick up noise, and that noise is real. If you have a system with lots of high sensitivity (high impedance) nodes and/or large PCB loop areas, then radiated switching noise can still be a problem for you.