I wonder why I saw a channel logo blinking very fast on some TV sets in a store.
You can barely notice it, but if you look directly at the logo, it's clearly there, especially if its bright on a dark scene.
Can I make it stop with some setting changes or just avoid those TV's?
You mean the watermark? If you saw it flashing, it could be a number of things. Could be from the source material (usually a blu-ray). Could be a bad distribution system. Could be bad cables. Or it could be the "motion enhancement" of that set, which if you ask anyone on here, that should be off.