The summary of the video says:
"Big question with the new Verizon LTE iPad was whether it would work with AT&Ts 3G network in the US. Worry no more!
"Of course it still won't work with ATTs LTE network but it's a great fallback when Verizon's LTE is not accessible!"
#1) If you have a NEW not yet activated iPad or iPhone microSIM and place it into a Verizon "new iPad" you cannot activate the SIM in the iPad --- or online on AT&T's site (the site will reject the IMEI number of the Verizon iPad, which makes sense as AT&T knows which are theirs).
#2) If you have an ACTIVATED iPhone or iPad microSIM and put it in the Verizon iPad, the ATT data will work, but you will have to change the APN settings on the device to match ATT's.
To change the APN settings, you just follow this Apple support doc. AT&T's APN settings (and others) can be found here.
However, you can bet this violates AT&T's terms of service.
Watch the video demo below.