In the suttas, the Buddha repeatedly said he taught Dhamma-Vinaya (teachings and discipline, in short). We do find rare Abhidhammic-type of text and classifications in the suttas, e.g. the 5th form-sphere jhāna, but we don't see common tinge of Abhidhamma in the Sutta Pitaka. E.g. the Nāmarūpa definition in the Sutta and Abhidhamma are different.
According to commentaries, the Buddha taught Abhidhamma, i.e. he taught Abhidhamma to the devas at Tāvatiṃsa Heaven, and his late birth mother, who was reborn as a deva in Tusita Heaven, come down to listen to the teachings. The Abhidhamma was subsequently taught to one of his chief disciple, Ven. Sāriputta.
Whether the Buddha directly taught Abhidhamma or not, if one was able to attain liberation by virtue of studying, contemplating, and practising according to the Suttas or Abhidhamma or both, in accordance to the 4 Noble Truths, it does not matter that much what happened nearly 2600 years ago. After all, all the suttas in existence today went through thousand of years of oral transmission, compilation, classification, and then written transmission; omissions and additions especially during later years are to be expected.
So,
@Ironside , do you think the Buddha taught Abhidhamma?