Sure, Rust does not require that your arbitrary string is actually safe HTML, a valid SQL string, XML element, DNS name and IPv4 address.
As a result, if you take arbitrary input, and then run it as an SQL query who knows what will happen, despite it being a memory safe language.
On the other hand, (safe) Rust has strong type checking, so you can make types named SafeHTML, ValidSQLString, XMLelement and so on, with the properties you desire enforced. This does not prevent the same idiots who try to make an SQL query using format!() from doing so, as they won't use ValidSQLString anyway.
If all strings fill you with such fear, probably General Purpose Programming languages aren't for you, maybe you will feel safer in WUFFS. It looks at first glance as though WUFFS has strings, but it actually doesn't, they're just a human readable label for WUFFS non-OK statuses (e.g. errors like "#bad Huffman code"). You can rest assured that your WUFFS code for processing a PDF can't have SQL injection for two reasons: 1. WUFFS doesn't have any strings to inject SQL into, and 2. WUFFS can't talk to an SQL database at all. In exchange for this safety you give up the ability to do anything outside the tiny sphere of interest of the language.