With the easy availability of any image from the 'net, many photoprinters / lithographers / t-shirt printers etc. will ask you to sign an agreement (or it will be implied as a condition of them completing your order) that you either own or are authorised to use the image that they are printing on your behalf. This would cover them in the event of a copyright issue arising, and put the blame firmly at your feet.
However, unless you were printing off several hundreds, or even thousands of copies of the image, and flogging them on-line or at your local market, then it is unlikely to be an issue. For a single T-shirt, I would not worry too much.
As for Getty Images, yes, they are a stock-image agency, and therefore manage the rights (for a fee) on behalf of the copyright holders - they do not (in most cases) own the copyright themselves, but act as agents in the distribution of both RF (Royalty-free) and RM (Rights Managed) images.