You're obviously talking about pressing down on a free-standing rim that hasn't been built into a tensioned wheel. Try that again with a fully tensioned built wheel. The spoke tension prevents any flexing of the rim, regardless of whether it's double-walled or single-walled. The late Jobst Brandt, a former Porsche engineer who wrote "The Bicycle Wheel," the first, definitive work on the forces at work in the structure of a bike wheel, determined that bike wheels will dent before they flex to any significant degree.

Quote from this page:

"If the wheel is strong enough for its intended use then its stiffness is more than adequate.

Since the stiffness of the frame, pedal-cranks and especially the tires is much lower than the wheel stiffness, the rider cannot possibly feel the minute differences in stiffness among different wheels. The "liveliness" attributed to "stiff" wheels is an acoustic phenomenon that results largely from light tires with high pressure and to a lesser degree on tight spokes. This mechanical resonance can be heard, and possibly felt, in the handlebars and is not related to wheel stiffness. Liveliness may have some merit but it does not result from certain spoke patterns and has nothing to do with wheel stiffness.

In summary, stiffness is generally not an issue to consider. A wheel that is strong enough to withstand the loads of its intended use, with a reasonable margin of safety, is stiff enough."