NACD and TDI does not have any such rule stating 800 ft. I don't know where that comes from. It is noted in the instructors standard to limit the dive of the first intro dive to 600 ft but after that hey the distance is there just stay out of deco. From the book itself On The Intro to Cave Class:
PURPOSE:
To develop basic cave diving skills with limited penetrations in the cave environment. This is the second level of the progression to the full cave diver certification. It is a recreational cave diving course. The course develops and establishes minimum skills, knowledge, dive planning abilities, problem solving procedures and the basic abilities necessary to safely cave dive to limited penetrations, using single tanks.
CAVE DIVES:
Intro to Cave diver certification is based on satisfactory performance of ALL skills listed in these standards by ALL students regardless of prior training. Students will complete a minimum of four cave dives for certification and at instructor discretion one open water evaluation dive. Students using double tanks will use 1/6 air rule. If certified at this level students must be informed they can only dive with a single tank.
LIMITS:
A. Penetration/ depth.
Dive one: 600 feet recommended
All succeeding dives: no penetration limit
Depth: 100 ft
B. Air rules - 1/3 air rules may be used for single tank dives. Students using doubles will use the
1/6 air rule
C. Minimum starting visibility thirty (30) feet.
D. Minor restrictions acceptable. (A minor restriction is when divers are prevented from traveling side by side, forces them into single file travel). No major restrictions.
E. It is highly recommended that additional dives be added at this level. The four dives are the minimum.