Sorry, the 10 yr anniversary of the L.A. riots just passed and I was feeling nostalgic...
This thread seems to be getting a little personal, but I would like to add my $0.02 anyway. First, I see limited situations where nonswimmers/weak swimmers may be OK to scuba dive. The Handicapped Scuba Association offers a structured program to introduce handicapped divers to the joys of scuba. The dives are offered under controlled conditions in warm/clear water areas. Divers of various disabilities are paired with HSA-trained buddies and DMs, after having been trained by HSA instructors. In this case, strong swimmers make up for the impaired abilities of the HSA divers. I can't wait to take my paraplegic friend diving!
However, outside of the very limited exception above, I firmly believe that weak swimmers and nonswimmers have no place in Scuba diving. If you are so passionate about the sport, you ought to take the time to learn how to swim and be comfortable in the ocean. In fact, prospective BOW students should try bodysurfing and freediving first in order to become accustomed to the ocean and improve water skills and confidence. There's nothing like diving under a big set of waves or bobbing around in the surf sans mask, fins and snorkel to introduce someone to the power of the ocean. Why the rush to blow bubbles with Scuba? If you're reasonably fit, a few swimming lessons and a coupla days at the beach can improve your skills and confidence dramatically.
I have assisted a fair number of classes in the Monterey area, and have noted a strong correlation between weak swimmers and panic situations. This is especially in AOW classes, where recently certified divers first encounter mildly challenging conditions such as night dives from the beach. I haven't seen a class yet where someone hasn't been towed back to the shore/boat by a stronger swimmer.
IMHO, all classes should require at least two free dives to a sandy bottom (say, 15-20'), coupled with surf entries and lost equipment recoveries. Scuba isn't a macho sport, and most people can learn the requisite skills, but it is more than cruising tropical reefs in fancy gear. You should be able to self rescue (i.e. swim for your life) in all but the most dire situations.