It's probably more about the trademark than the domain. The other company applied for the Groupon trademark as well, so trading under that name until the trademark dispute is settled could be quite problematic and using a different name wouldn't be able to leverage the Groupon brand.

Couldn't agree more. Apple doesn't own apple.co.uk so they just use apple.com/uk and use geoip to make apple.com (by default, can override country) redirect.

I don't know how australians perceive it but in the uk people wouldn't care or read anything into it if it was a .co.uk or a .com

Launching a completely different brand seems unnecessary and sub-optimal.

facebook.com.au redirects to facebook.