Thanks for the update, otherwise I would've found myself frustrated and confused! I used to find it faster (and more enjoyable) walking from BART through International to Terminal 1, but looks like I'm taking the AirTrain now...
You may still wish to walk from BART to T1. It's only slightly longer to do that clockwise via T3 and T2. I walk outside on the sidewalk at the start of T3 as it's a little shorter and less congested.