When you make a connection to the city sewers or to the power company, there is some kind of pre-connection step where the terms are presented and you agree to those terms.
With HTTP and LinkedIn, there is no such step. There's no pre-connection agreement. LinkedIn could present such an agreement on first connection, but they do not.
That argument has been tried in a variety of ways and been shot down in court repeatedly. (there are parallels to tenants not agreeing to the terms of their internet connection where the landlord provided it).
LinkedIn has two things that they do which protect them; First, they specify they disallow access in their robots.txt file. While not a binding agreement per se it is the default mechanism that is accepted by the community for apriori identifying whether or not automated access is possible. Second, when they detect an access pattern that violates their terms of service they actively block the access proactively notify the source of the violation.
The sad truth is that web scraping has been around since the very beginnings of the Web back in 1993 and this question has been litigated in every way that you might choose to argue it, the body of case law is enough to fill at least two volumes in the reference section of the library.
There is no legal or ethical basis for scraping the web without permission. And if it isn't explicitly allowed by a site the presumption is that it is disallowed (no 'open door' exception).
When you make your conenction to Linkedin, What user agent would you provide? One that's blank, another that's "lelandbatey bot" or one that says, "Mozilla/5.0 (iPad; U; CPU OS 3_2_1 like Mac OS X; en-us) AppleWebKit/531.21.10 (KHTML, like Gecko) Mobile/7B405" ?
You agree to the terms of service when you sign up.
If you're talking about making anonymous requests to their service, they only allow a few of those before they stop showing you profiles. If you circumvent that protection, it's a bit more like hooking a cable up to a power line (illegal) or dumping your commercial waste in the sewer (illegal).
With HTTP and LinkedIn, there is no such step. There's no pre-connection agreement. LinkedIn could present such an agreement on first connection, but they do not.