I'd guess that you were OK to descend as soon as you intercepted the
inbound course,

Argh! No! The PILOT must know when he's established and within the
protected area. All you've intercepted is a navaid, not a segment of
the approach, until you've reached the start of that segment.

they intend for me to follow any altitude instructions as soon as
I'm on the course, even if I won't be inside PT limits for another 10
minutes or more.

What ATC intends is irrelevant. If they want you at the published
altitude before you reached the point where that altitude applies,
then they're got to clear you down to it, using their MVAs.

Failure to understand this concept has killed some people in the past,
including at least 1 airliner, TWA 514.

See the AOPA article:

http://www.aopa.org/asf/asfarticles/sp9806.html