Google is actually much more terrifying in that they have more information about me than any other entity (Search, Gmail, Google Analytics, Chrome, GChat, etc.) Yet, I tend not to give it much thought.
Some people are upset about LinkedIn spam - but that's never been a problem for me. I haven't figured out a good answer to this yet.
1) Google has a proven track record with email and email security (Gmail) over many years now
2) LinkedIn has a bad reputation for security
3) Most of the people I know who use LinkedIn probably wouldn't even have thought "how does this work". I don't like that any company can "get away with" something like this that could put so many peoples' jobs at risk. It feels shady and unfair.
To the average user, LinkedIn made no attempt what so ever to explain that by doing this, you were putting approximately the same level of trust in them as you do in Google/some other mail provider. This is particularly troubling if most people, as I do, don't have an existing trust relationship with LinkedIn simply because everything we have on their is public.