I made the same argument when this came up a few years ago. It turns out that I wasn't entirely correct, and neither are you.
While it's true that mixing a strong bleach solution with a strong acid is a HORRIBLE (and potentially lethal) idea, lowering the pH of a mild bleach sanitizing solution with vinegar can be safe and effective. It's important to note that the bleach solution must be fairly dilute before the addition of any acid. I'll see if I can dig up a source for you.
EDIT: Source(s)
http://www.eurekalert.org/pub_releases/2006-02/asfm-vik021306.php
I wish I could find the chemical equation that I remember someone posting. It showed the reason that dilute bleach and dilute acids can mix safely without liberating chlorine gas. However, I'm coming up empty handed, and I'm no chemistry major.
Wither a chemical is a weak vs a strong acid or base is not dependent on the concentration (dilution) molarity of the aqueous solution, but is dependent on the chemicals ability to gain or release hydrogen protons. Bleach is considered a "strong" base and acetic acid (vinegar) is considered a "weak" acid. however, it is reactive enough with bleach to release chlorine gas.
What Happens When Bleach and Vinegar Are Mixed
Chlorine bleach contains sodium hypochlorite or NaOCl. Because bleach is sodium hypochlorite in water, the sodium hypochlorite in bleach actually exists as hypochlorous acid:
NaOCl + H2O ↔ HOCl + Na+ + OH-
Hypochlorous acid is a strong oxidizer. This is what makes it so good at bleaching and disinfection. If you mix bleach with an acid, chlorine gas will be produced. For example, if you mix bleach with toilet bowl cleaner, which contains hydrochloric acid:
HOCl + HCl ↔ H2O + Cl2
Chlorine gas attacks mucous membranes, such as your eyes, throat, and lungs and can kill you, so causing that reaction isn't in your best interest. If you mix bleach with another acid, such as the acetic acid found in vinegar, you get essentially the same result:
2HOCl + 2HAc ↔ Cl2 + 2H2O + 2Ac- (Ac : CH3COO)
There is an equilibrium between the chlorine species that is influenced by pH. When the pH is lowered, as by adding toilet bowl cleaner or vinegar, the ratio of chlorine gas in increased. When the pH is raised, the ratio of hypochlorite ion is increased. Hypochlorite ion is a less efficient oxidizer than hypochlorous acid, so some people will intentionally lower the pH of bleach to increase the oxidizing power of the chemical, even though chlorine gas is produced as a result.
I don't know how dilute these chemicals would need to be in order "safely" combine these chemicals, but I think this falls into the catagory of "please don't try this at home".