Run fitness complimenting bike fitness?

My first triathlon about 10 years ago I did the huge aerobic base thing that Shane referred to.  I was a runner at the time averaging 1 hour 24 minute half marathons and 18 minute 15 second 5K's.  I didn't have access to a pool and didn't have a street bike but some friends were all signing up together to do a spring triathlon and wanted me in the group with them so we could motivate each other as we trained and just enjoy doing something together on race day.

I was not in a good position to do any swim training and decided to not do any bike training on my beast of a mountain bike either to see how well I could be in a swim and bike leg with only run training.  So I followed my favorite 16 week half marathon plan.  I borrowed a high end street race bike for the race and bought some Speedo jammer shorts, a compression shirt, goggle, and a swim cap the night before the race.  

No amount of running fitness could have made me faster on the swim.  My form and body position were so bad that I only was getting enough air with each breath to go about 40 meter with the front crawl.  After that I switched to the side stroke.  I was working that stroke hard but was more than twice the swim time of the top people of the day.   So...for swimming. Spend more time on your swim form and less time running if you want to go faster.

I was flying on that bike.  I felt really pressed to make up for lost time and was really cooking it.  My average speed was round 21 MPH which was front of the pack.  Running seemed to have a lot of cross over to cycling.

When I came of the bike my legs felt like jello.  My legs would not move naturally.  I mental was trying to imagine how my legs should move to run and then was trying to force them to make those movements.  It felt like my legs were hobbled together with strong rubber tubing.  I had pretty much abandoned any chance or getting a respectable run time until I saw a friend (who started the swim about 30 minuted ahead of me and was already done with the race) cheer me on and tell me that I had the run.  The run was all I had trained for so I decided to give it my best.  The jello feeling never went away.  Moving my legs in a running motion never got easier but I didn't give up.  My run time was around 20 minutes flat.  So about 2 minutes over my open run time.  I was pretty disappointing until I learned it was the 2nd fastest run time of the over 300 people in the race and that I had bit three guys at the race were faster open runners than me (but not Triathletes either) and one triathlete (who was almost as fast as me as an open runner).  So even if your run and bike fitness are sub par and even if you over cook it on the bike if you have strong run fitness you can pull out a respectable run.  11-12% over my open run time isn't a really good run time. something under 8% over my open run time is what I would like to be doing in every race.  I do feel that improved fitness from running benefit you in swimming and cycling, but if you are trading out swimming and cycling training type for running type then you aren't increasing your fitness.  You are just achieving it through a different focus.  If that is what you are doing you aren't likely to so any improvements in Cycling or swimming.