Command block activating without redstone (even though set to "Need redstone")

I am finding that command blocks that are not sending redstone signals are still activating adjacent command blocks that are set to "Need redstone".  

Example command block A is set to "Impulse", "unconditional", "Needs Redstone".  It contains a "execute" command that reports pass or fail

Command block B is set to "Impulse", "conditional", "Needs redstone".  The block behind it is A.   It contains just a "say" command. 

When a redstone signal is sent to B from another source (not A), the execute command of A fires anyway.  Yet the "say command" when it fires is not sending out a redstone signal (no adjacent redstone lights up)

A should not be firing but it is