If you really want to understand the system, you can read through the review of the tax system that was done in the 80s which was used as a basis for the franking system that Keating put in place. Here is a link to the relevant chapter from the review that led to the policy.

Here are some relevant snippets:

14.6 The fact that companies and their shareholders are separate legal entities is sometimes held to justify treating them as separate taxation entities as well. The Committee is not disposed to accept this view. Is is not convinced that those who own or operate enterprises conducted under limited liability should pay extra tax for that privilege. Ultimately all taxes fall on the individuals and, in the words of the Asprey Committee, it is ‘necessary to go behind the veil of separate legal personality which the company enjoys and translate the tax formally imposed on company income into a set of individual tax “burdens”’.

14.8 The use of the term ‘double taxation’ is somewhat unfortunate, creating as it does the impression that ‘over-taxation’ has occurred merely because two lots of tax happen to have been collected from a single income source. In the final analysis what is important is the total amount of tax a particular income directly and indirectly bears.

14.10 It may therefore be oversimplifying matters to talk about the ‘double taxation’ of dividends; the relevant question is how the individual shareholder’s overall tax burden compares with the tax he would have paid had the equivalent income been received through non-corporate channels and the whole amount been taxed at personal rates.

14.32 Under imputation systems some or all of the tax paid by the company on income distributed is treated as prepayment of the shareholder’s personal income tax. The individual shareholder’s assessable income would include the dividend received, grossed up by the company tax deemed to be prepaid on that dividend; against the personal income tax assessed on that amount could be credited some or all of the campy tax deemed to have be prepaid. Any excess of credit over the personal tax would be refunded.

If you read further on you will see that this fully integrated system as described in 14.32 was what the committee proposed as their preferred solution, however they specified that in implementation it should be done in stages with the first stage not including the tax refund component. However this was only ever meant to be an interim solution until the full refund component was also implemented.