canreinvite is an obsolete alternative name for directmedia.
It controls whether Asterisk will issue a SIP Re-INVITE, to change the media destination to go direct to the other party, rather than through Asterisk. This reduces the load on Asterisk, and the network near to it. It will be ignored if Asterisk needs to monitor the media or RFC 2833/4733 DTMF signalling streams, or if there are no codecs in common between the two sides.
Call recording, listening in, and enabling any DTMF controlled features will normally inhibit the use of direct media.