My unmodified tinkering skill is 643. The Adv Vetrovian Tinkerer Vol V only requires 625. My character is also level 125 Alchemist that completed the Vetrovian tradeskill quests. What else do I need to scribe this?
Pretty sure that's not your unmodified skill, since that maxes out at 625. Any AAs or gear that boost tinkering don't count when it comes to scribing stuff. Open your Character window, go to the Skills tab, then the Tradeskill tab and scroll to the bottom and look at the Tinkering skill:
It's way past time they addressed this in the interface. When it shows you a modified stat there needs to be a way to see a list of what's modifying it. Having to go through every piece of gear and every AA to work it out is a nightmare. Or at the very least list the base stat alongside the modified to avoid this particular problem.