You're correct jbarnes.
For unlimited T welder qual, refer to Figure 4.21 for all position or the optional Figure 4.29 Horizontal position test configuration where you'll see the thickness of the plate being 1"
For limited Thickness welder qual, refer to figure 4.30 for all position or the optional 4.31 Horizontal position test configuration that clearly shows a 3/8" plate T...
Table 4.10 does describe the limit for a 3/8" T plate, showing a Minimum of 1/8"T & maximum T of 3/4" with a reference to note 3.
The caveat to this is if the T of plate is: 3/8"< T< 1" then the maximum T is 2T with a reference to note 3 also.
Note 3: Also qualifies for welding any fillet or PJP weld size on any thickness of plate, pipe or tubing...
Now if you look below(1) "Test on Plate," you'll notice another section which refers to Production Fillet welds (T-joint and Skewed)... I believe the person who's disputing your claim is inadvertently referring to that section instead because in that section, you'll notice that it shows a groove for the first three types of test welds and the first one shows a "Nominal Test Plate Thickness, T, in." of 3/8" and if you go across to find the "Nominal Plate Thickness qualified, in." and it shows a maximum of "unlimited" which is probably why there's a debate in the first place... In other words, right table, wrong category.
HENRY