You are quite correct. Neither OSHA or ANSI/ASME standards require annual load testing of overhead cranes used in general industry. Load testing is only required for new cranes and those which have been extensively repaired or altered. The term "extensively repaired" can be open to interpretation, however normal maintenance activities would not be included (such as wire rope replacement). It is also interesting to note that current OSHA standards (1910.179) now allow load testing (when required) at 100 percent of capacity in lieu of the old 125 percent figure.
There is a letter of interpretation from ANSI/ASME that does discuss this issue (ANSI/ASME B30.2). It was included in one of the older issues of that standard (or perhaps one of the addedums). In that letter, they state quite clearly that such annual load testing is not required.