This is mostly right. Time served to pay off one educational benefit (in this case, active duty time used to pay off your HPSP scholarship) cannot be applied to another educational benefit. However, intern year is neutral for HPSP purposes, so it should count for GI Bill. Here's an illustration:
- I took a two-year HPSP scholarship
- PGY-1: one year toward GI Bill, no time toward HPSP
- PGY-2: one year toward HPSP, no time toward GI Bill
- PGY-3: one year toward HPSP, no time toward GI Bill
- PGY-4: one year toward GI Bill, HPSP already paid off
- First year as attending: one year toward GI Bill
So I became eligible for 100% GI Bill benefits after completing my first year as an attending.
Also note that the VA rates your eligibility at the time you apply for benefits, not the time you plan to start school. If you will become eligible for 100% in August but submit your paperwork to the VA in July, for example, you'll be rated for 90% benefits -- even if your matriculation date is in September.
One final thing: if you start receiving your benefits while still on active duty but then separate while you're still receiving them, notify the VA! As a civilian, you're eligible to receive a housing stipend that you can't get while you're still receiving your BAH.