I know Nick Wyman and can assure you that there is NO chance that he (or the union or BCEFA)is being paid off by Julie Taymor.
The actual possibility of Equity being sued because of what would ultimately be the creative team's negligence is equally absurd. The union has done more than "due diligence" in regards to Spiderman. Believe me, this show is under a lot more scrutiny from the union than meets the eye. The relationship between the team and the Union hierarchy isn't as rosy as the public statements suggest. There is a lot more than three blocks difference between what is happening on 43rd street and what is happening on 46th.
Having said all this, remember that although the safety of the actors is the primary concern, job security is also another. Regardless of its artistic merit (over which Equity has no control and is not at liberty as a body to act upon) Spiderman has the potential to employ hundreds of union members. It is in everyone's best interest to make this show safe and to keep these actors working. That is Wyman's goal.
Other than that, did you enjoy the play Mrs Lincoln?