According to RFC3986, URIs (the proper name; URLs are a kind of URI) are correctly of the form:
<scheme>:<scheme-specific-part>
For some schemes, the <scheme-specific-part> may contain a <hierarchical-part>, the format for which is: //<authority>[/<path>] | <path>
So it's only hierarchical URIs with a defined authority that have the (admittedly iconic) "://" in them.I know most people identity URIs as having that sequence in them, but these are all valid URIs:
mailto:bob@example.com
sip:bob@example.com
tel:+18005550123
file:/path/to/file
I'm not saying I expect everyone to understand these subtleties, but people who claim to grok URLs ought to.