At least the nurse who did the sutures was cute! (Is that over the edge for this forum? If so, I apologize in advance.)
Not over the edge at all.
Focus on the positive, cute nurse, all fingers still attached.
I started framing in Chicago in 1969. Two blocks from Wrigley Field.
I regularly cut glass out of 40 x 60 and have not had one shatter like that.
You may have had a slight crack or chip on the edge that ran.
I have a glass seamer, but I don't use it on regular frame jobs, only for jobs with glass and clips or Uni-Frames which are few and far between. (thank goodness)
I always clean the glass outside of the frame. The glass needs to be properly supported if you pick it up when it's flat on the table. (not really recommended on really large pieces)
Support it with the backing as previously mentioned and if you have to pick it up horizontally, spread your fingers wide apart to minimize the stress. If you try to pick up a large sheet with your hand at one spot it can break off because of the stress in that small area. Spreading your fingers and/or using a backing will spread out the stress over a larger area.
It's also a good idea on large pieces, as mentioned earlier, to stand the frame up and lean it against the fitting table and put the glass and art package into the frame in a vertical position.
Shoot it in and then put it on the table for backing and wire.