Modigliani-Miller refers to the financial structure of your corporation, GE in this case: it refers to the mix of capital that GE raises from investors (debt + equity). To give a simple example to illustrate, the value of your lemonade stand as a business is based on your revenue minus your costs, it's based on your "business". You need to raise money to buy your raw materials and equipment to get started or expand? Whether you borrow that money or sell shares in your lemonade stand does not change the value of your business. The bit about absence of tax incentives is because you can write off the interest on debt from the income taxes, but the dividends you pay actually get taxed, so there is an incentive for the equity holders to raise some money via debt rather than equity; but the point that M&M makes remains true.
GE Capital did not fund GE, so M&M doesn't apply.
M&M would apply to GE's ownership of GE Capital, but if all the debt and equity is owned by one entity there really isn't a difference between them (see Humpty Dumpty, back together again).
It's quite common for large industrial companies to have large credit arms: oil companies extend credit to gas stations to buy their gas, just like automobile manufacturers finance car purchases. GE was no different. Leveraging their expertise in finance was a natural extension of the business, and financial firms sometimes fail like any other business, whether they are standalone or wholly owned subsidiaries.
