Quote:
Is it the same idea as behind the US?
No. The grill on US stamps is produced by puncturing the paper, allowing the cancel ink to get into the stamp paper and thereby making it harder to remove. It's purpose was to keep used stamps from being reused as postage. Turned out it wasn't feasible, so they quite doing that.
The grilled gum on Swiss stamps was used as a method to keep the stamp from curling. This is the equivalent of gum breakers on mid-20th century US stamps.
The gum breakers on US stamps have relatively wide spacings (typically >1 centimeter). While the gum is still on the stamp, you will see slight "bends" where the gum breaker is at. However, once the gum is removed, the paper bends will disappear. That is why you do not see gum breaker paper bends on used stamps or on unused no gum stamps.
The grilled gum on Swiss stamps has spacings of <1 millimeter. This does produce a permanent effect on the paper. So even when the gum is removed, you can still see the fine mesh-like pattern on the paper.