"So does that mean that before the packet goes onto the trunk link it is put into the native VLAN then when it exits the trunk link (on the other side) it is stripped of the VLAN info? "
No, what your prior quotation decribed is what a switch should do with untagged frames received on a port defined as a VLAN trunk.
The VLAN tags informs the switch what VLAN a frames belongs to when it is received on a VLAN trunk port, but without such a tag, how does the switch know the intended VLAN? It doesn't, from the frame itself. So, we can often configure a trunk port to place any untagged frames into one VLAN of our choice. In theory, once we define what VLAN untagged frames will be considered a member of, tagged frames, for that VLAN could also be accepted. Both should be treated the same by the receiving switch.
As for a switch sending packets out a VLAN trunk, normally you would expect all packets to be VLAN tagged although a switch might support sending one particular VLAN frames without tags to support a device, such as the PC described in your quotation, that doesn't understand how to process, or expect, tagged frames.
If you're wondering how this all comes to be, consider a PC that knows nothing about VLAN tags is connected to an IP phone which does (which connects to the network) and you want to place the two devices on different VLANs. As the PC traffic transits the phone could, in theory, wrap/unwrap the PC traffic with VLANs tags when working with the network switch. However, if the phone fails, you can design the IP phone hardware to keep the link good from PC to the network, but then the IP phone PC VLAN processing would be lost. So for that reason, and the reason, we might want to add/remove an IP phone "in front" of the PC, we want to continue to support untagged frames to/from the PC.
Altough the frames to the PC are untagged, since we can configure what VLAN untagged frame should be considered per port, we can have different PCs (on different ports) in different VLANs on the switch. (This is very similar to port based VLANs, but instead of being limited to one logical VLAN per port, we're limited to one untagged VLAN per port but can have multiple tagged VLANs per port.)
