Should a link opened/closed by a chain-breaker be stiff afterwards?
Only if you didn't relieve the link after putting it back together.  It's standard procedure (if you read the instructions that came with the tool) -- you stick the chain tool into the "stiff" link so that the anvil is BETWEEN the sides of the link and only catches the near face, then crank the tool's pin down VERY SLIGHTLY against the chain pin, just enough to create some play.