And even to toss in another layer to this - as Matthew said:
So, is there an AEA rule about an actor video taping another actor - I don't think there is . . .
For Ballet Companies - we sign contracts with choreographers, Rights and Trusts - and there are very specific rules about videotaping, even from the wings, of the choreography. If anyone (including a performer) videos the performance, or any portion thereof, from anywhere - and that video gets posted online, and is discovered - the company that signed the contract for the rights to that ballet can lose their license rights.
For us, this is a major issue in our company - and it's up to the management to explain this situation to the performers and enforce it. So, speaking from that side, the answer is no. And they shouldn't be videoing the performance anyway. Period.
However - if this video is of backstage antics - be it nothing to do with the actual performance - that's another matter. How does the company (producer or performers) wish to be perceived in social media? Even if posted privately, the video can get out easily. That's a branding concern that also has to be handled by company policy.