Just be aware that this is not the official policy in the US.
The only avenue to data preservation under the program is mail-in service send them your broken TC you get one back with your data on it. They repeatedly refused to let me do what RedTomato did and I complained about my privacy. Ultimately they just shipped me a refurb replacement and did not request the old one back.
I chatted to them online first, and same as you, they repeatedly refused to let me do it. So I thought sod it, opened it up (carefully!), copied my data, wiped it, put it back.
Then in the apple store, I was talking to the guy, after he'd agreed to replace it, and thought I'd just casually ask for my old drive back. Nothing ventured, nothing gained or lost. 'Sure! I'll just get you your old drive back from downstairs. Just give me a minute!'
So. Unofficial. And may depend on who you get.