A lot depends on the type clay that you have, here in Texas we have Red, White, Black and mixes of all the above. Suzi is right, in most cases if there is not enough sand mixed in it will "cake" and hold water. Digging a larger hole and using a "Filler" is like putting mulch or potting soil, or dirt in a reservoir, it will still hold water. I have a white clay, I planted 12 trees, dug up 6 on the lower end of the lot to keep them from drowning. The balance is doing okay, not great but okay. I believe the main issue that I have is the cakeing is restricting the roots. Since that particular area seems to drain okay I am going to go back and dig a ring about 2 feet deep, 3 ft out from the trunk and amend the soil. I think mature roots will penetrate the clay but the young will not.
Disclaimer - I do not know what I am talking about, do your own homework and experiments based on what you find.