That's a very interesting interpretation of the linked papers.
While timing information may make brute force attacks against the passwords easier, it is not feasible to reconstruct passwords based on the timing information exposed by Ebay.
It is also worth noting that the ability to perform more efficient brute force searches doesn't really matter in the case of Ebay, as it will not make such attacks feasible over the internet.
This attack depends on being able to identify individual keys so it's not really applicable here. However, a similar attack might be possible here if not for the very small sample size.
It is feasible to reconstruct passwords from timing information alone. This has been done against e.g.
SSH http://people.eecs.berkeley.edu/~daw/papers/ssh-use01.pdf and
TLS https://www.schneier.com/blog/archives/2010/03/side-channel_...