Company policy states you can not solicit for anything on UPS property, all union activity must be posted on the union bulletin board. So if this is UPS owned/leased property, whoever put them there is breaking UPS rules. Now if UPS doesn't own/lease property, then shame on him.
This might be company policy, but is entirely against the spirit of the protections under the NLRA. There was actually a fairly significant case in the early 2000's regarding a TDU member that was also a UPS Driver passing out the Convoy Dispatch in a "mixed use" work area off-the-clock. UPS sent the TDU member a warning letter and their case went to the NLRB; UPS had to remove the discipline from the member's record.
The case file number for a good example of this is 07-CA-041784 from Saginaw, MI and is on NLRB.gov
Long story short, you can absolutely hand out union related material/handbills/grievance forms/etc. or petitions as long as you're not in a work area and not on the clock. A mixed used area consists of a place where employees congregate and
might be on the clock (ie waiting for instructions/assignments). You could stand near the time clocks and catch members punching in before their start time or use the break rooms. You cannot, however, go "truck to truck" or interrupt members while working.
Video taping is a different story. I'm not familiar with any NLRB case upholding an employee's right to video tape on company premises. The only thing I could thing of would be some sort of whistle blower protection for egregious safety violations but this doesn't apply -- other people witnessing the 623 trustee would be just as effective as a video and doesn't carry the risk of getting fired.