More anecdotes in the favor of the new glass:

My mom went through a glass door as a kid.

This was in the mid- to late-70s. While she didn't have it as bad as the kid you describe, she had an 18" long, 4" wide (at its widest point) shard of glass sticking out of her back. Add to that multiple areas where smaller shards, splinters, and slivers got stuck in her arms, shoulders, chest, and back. She still has scars on her back from where the only way they had to remove all the tiny bits of glass in those areas was a melon baller -like device that pulled out fat, skin, and muscle as well. They did not give her local anesthetic or put her under for this. She was awake and feeling it every moment. When the doctors gave her stitches, they stopped counting after 150.

In not nearly as painful an incident, my sister went through a glass storm door while filming a story for a school project at home. My parents either didn't care or didn't know that those storm doors weren't safety glass.

So, my sister goes arms and shoulders through the door, pulls back out, and then proceeds to walk out the door. I hear her scream, then go check on her. No glass that I could see sticking out anywhere, but a few shards had cut her bicep area in the shape of a bird's foot. She had been cut so deeply that I could see fat between flaps of her skin.

Her project group panicked. I sent one to get my dad, one to get towels out of the kitchen, and had one stay there to talk to my sister so that she wouldn't look at all the smaller cuts...or try to see the big one. Once her friend got to me with the towels, I cleaned the blood away from the wounds so I could see if there's any large pieces of glass in there to worry about. I didn't see any.

I tied one of the kitchen towels around the big wound just tightly enough to apply pressure, but not tight enough to make it a tourniquet. The other wounds, I just applied pressure to with a towel. About that time, my dad showed up and takes her to the hospital where they had to give her X-Rays before they'll giver her stitches, just to be sure there's no shards of glass. She got lucky, she had none.

Of her smaller cuts, she should have probably had stitches on one of them. She now has a thick, ropy scar that runs almost from elbow to wrist on the outside of her arm. The rest of them are also thick and ropy, but not nearly as large. The bigger wound on her arm is now a scar the size of a quarter. In that wound alone she got 25 stitches.

TL;DR: My mom ran through a glass door, had a shard of glass 18" long, 4" wide (at its widest point) stuck in her back, had to have smaller shards removed with a melon baller type thing, and had over 150 stitches on all the cuts. My sister ran through a glass (not safety glass) door more recently, didn't get nearly as cut up as my mom did, but got cut deeply.