Since my previous test and Alex234 tests didn't gave the same conclusion I went back to the dummy for 2 sessions of around 2k pet attacks. On both sessions I had the same talent spec with 0/3 FA. I turned the autocast for all pet abilities off, except for Claw.
Session 1:
263 hit (same as Alex234 used).
1192 Melee hits, 0 missed
810 Claw hits, 0 missed
Recount
So this is the same as Alex234 found. So with 263 your pet is hitcapped!
Session 2:
262 hit (same as I used yesterday)
1166 Melee hits, 12 missed.
873 Claw hits, 8 missed.
Recount
20/(1166+873)*100% = 1.0%.
This is really not what anyone would expect, but it seems that 1 (specific) extra hit rating is giving pets a full 1% increased hit chance!
I think the sample size is big enough now to conclude that pets still have around 1% miss chance at 262 (7.99%) hit and are capped at 263 (8.02%). If anyone disagrees, feel free to test this yourself with bigger sample sizes, but I convinced myself.
This also means that it is better to be over the hitcap than just below. 262 might look good enough in the tooltip, but I would advice to always get atleast 263 hit. Better a few hit rating above 263 then just below 263, because you get a whole 1% pet miss for free by going to 263 hit or higher!