A tor2web proxy is just like any other piece of network infrastructure; it just passes back and forth requests and responses and doesn't inspect or modify content.
17 USC 512(a) (part of the DMCA) says:
A service provider shall not be liable ... for infringement of copyright by reason of the provider's transmitting, routing, or providing connections for, material through a system ... operated by or for the service provider, or by reason of the intermediate and transient storage of that material in the course of such transmitting, routing, or providing connections, if --
the transmission of the material was initiated by or at the direction of a person other than the service provider;
the transmission ... is carried out through an automatic technical process without selection of the material by the service provider;
the service provider does not select the recipients of the material except as an automatic response to the request of another person;
no copy of the material made ... is maintained ... in a manner ordinarily accessible to anyone other than anticipated recipients [or] for a longer period than is reasonably necessary for the transmission...
the material is transmitted ... without modification of its content.
512(b) extends the immunity to "generally accepted industry standard" caching.
(The DMCA takedown notice procedures you may have heard of are part of 512(c) and only apply to services that store copies of material.)
For more information, see the Tor legal FAQ.