So you're accusing Whaley (along with both of the Davis girls) of telling porkie pies in order to better set up Saint Lee of the Oswalds.
The Whaley issue is really odd and goes nowhere, if Oswald used public transport to get the the rooming house that has absolutely no bearing on his guilt and the only real viable alternative is that Oswald had a getaway car which has a huge impact on his guilt. Besides Oswald eventually admitted getting on and off a bus and catching a cab because he's not as desperate as these CT's and realized that it has little impact on his guilt.
And the Davis girls just happened to live a couple of doors down from a random killing but somehow they became involved within hours and they both had to quickly make up some story and because poor Virginia made a simple "typo" she is accused of being the spawn of Satan! You can't make this up, these Kooks are comedy Gold!
JohnM