But if he really was alone, then he had to take public transport back to his rooming house so why make that up and why do you doubt Oswald admitting he did exactly that?
It depends on what EXACTLY he told them:
---------------Bus ride(s) only
---------------Abortive bus ride followed by cab ride
---------------A. N. Other gave him a ride
The many problems with Mr Whaley's statements raise serious doubts as to the middle answer above, which is the official story of what Mr Oswald said. And the interrogation reports claim he only 'admitted' this the following day. Why would even a guilty Mr Oswald have wished to hide the fact that he had gotten a cab?
IF Mr Oswald told them something that suggested assistance from someone neither a bus driver nor a cab driver AND/OR ruled him out as the shooter of Officer Tippit, and if his claim were verified, then this claim would have been suppressed and a new, improved one put in his mouth in the interrogation reports.
Again, all that mattered was a lone nut narrative that could be sold to the public