"Google was directly targeting my old org."
It's possible, but what I've heard and seen is that many are shopping for where they'd like to work and that Amazon, Microsoft, Google, Salesforce and Workday are all on the shortlist. If one person in a department leaves for a specific competitor, it can raise the chances that others will look at the same place. I left a while ago for a competitor and I've received quite a few calls asking about what it is like and/or how to get in.
Oracle had many of it's employees sign a non-solicit agreement when they were hired, so actively recruiting peers after leaving for a competitor is legally risky behavior. That includes giving a list of names for recruiters to target. I can tell you that the competitor I now work for specifically won't accept any referrals/recommendations/information from me about Oracle employees because they know about the non-solicit and don't want any part of it either.
That all being said, there is a demand for experience and expertise by the companies on the "shortlist" and by other strong options as well. The key word there is "expertise" as Oracle's technology is very narrow, is lagging behind the market and has some significant gaps, so if you are looking to go somewhere else (either soon or after you receive a severance package), it is vital that you invest in your knowledge and skills in order to be relevant and marketable.