Yes but there are degrees with these things. If you attempt to open a locked door they don't charge you with armed robbery, even if that door has a sign that says "employee's only". I'm not suggesting attempting a SQL injection should just be ignored, but it should clearly be at worst a misdemeanor and not a felony, about on par with trespassing in terms of severity. Now, if you then use that SQL injection to steal protected data, gain further access, or delete data, then yeah you're talking about moving into felony territory.

Web servers are other peoples property, but they're also a public space when you open then up to the public by hosting public services on them. A private server is different from a public server in the same way private property is different from a public storefront. By making your server accessible to the public you lose some of the expectations of privacy and implicitly allow a certain degree of access.