They’re right to an extent, but for the wrong reason. Alkalines leak, unlike zinc-based batteries. They can destroy circuits especially when they’re left in too long, as seen in clocks, remotes, flashlights, etc.
“Can deliver too much current?” It’s true that alkaines have a higher capacity and lower resistance than zinc batteries, but as Halo said, if the clock’s current draw depends on the battery’s internal resistance, something’s not right.