If I have this right, once the tax inversion is done, corporations with foreign cash that they could not bring back to the US without being taxed again on it - will be able to do that tax free.
Not true—profits transferred by a foreign-domiciled company to a US subsidiary (generally in the form of an internal dividend payment) are taxed at the US rate.
However, a foreign-domiciled company has its parent holding company located outside the US, and hence it does not need to transfer cash to the US in order to pay dividends and repurchase shares. These are two of the main uses of cash that create problems for US-domiciled companies who are trying to avoid the US tax surcharge on profits already taxed in a foreign subsidiary.