A week of notice to move ~250TByte out is definitely unreasonable. 250TiB in 7 full days is an average of over 3.6Gbit/s, assuming no transfer interruptions and that he started immediately (i.e. already had other storage options lined up, and started transferring the second the notification email was sent).

For a company like Google several Gbit/s constantly over a week, or even the tens of Gbit/s needed to finish in one day, is not troublesome, but for most other people/entities it is completely unrealistic. Getting that much storage with that much bandwidth to it is far from impossible, but it won't be cheap, especially given he'd need it right this second.