One issue here is that recaptcha's traffic signature allows for a passive attacker. So instead of needing to modify the website a user visits, or trick them in

One issue here is that recaptcha's traffic signature allows for a passive attacker. So instead of needing to modify the website a user visits, or trick them into going to a domain you control, you are able to just look at the traffic logs and identify them without them knowing. I'm not too sure about what defines the "distinctive" signature of recaptcha, but I expect timing of when packets of certain sizes were sent (e.g. loading 9 images in quick succession will generate larger packets, and then you often get the incremental couple images with human-length delays between them).