Statcounter Invisible Links: Problem or not?

[Biggy]

Have a couple of questions:

1.

I'm using Statcounter tracker and the code comes with invisible link to statcounter homepage. Could this be giving a wrong flag to the SE's particularly Google? (The code has been there for couple of years)

2.

Also related to this, I'm looking for a tracker and Google Analytics comes to my mind first but I'm concerned of giving away too much details to Google on traffic details. Am I paranoid on this and should go ahead with google analytics?

thx.

[CainIV]

I already opt for the no link option with SC. I doubt this should be causing a problem because SC is older and has alot of inbound links on its own, but I never personally seen the point in giving them a direct link.