I have the same problem as the OP. Not on my 4Rnr; I can draw samples out of it perfectly. Problem is with my wife's '08 300 Touring. Engine is the Chrysler 3.5L SOHC HO V6 (EGG). I put the 1/4" tube down the dipstick tube, but it "bottoms out" about 3" shorter than the length of the dipstick. Thus, somewhere deep down in this engine's dipstick tube, there's a constriction that will NOT allow the pump's 1/4" collection tube to pass beyond. Her car is consistently more of a pain in the a** to work on than my old 4Rnr!
Blackstone says their pump's tubing is standard 1/4" refrigerator tubing (icemaker supply line - I'm guessing - anyway doesn't matter). I will try the suggestion above and see if my Napa shop has any 3/16" tubing to see if smaller diameter tubing works. Will keep this thread forum posted.
Alternate work-around thoughts & suggestions are welcome (however, it is NOT realistic or feasible for me to collect a midstream sample by removing the oil pan's drain plug; others may have a nice garage and jacks, but this is NOT an option available to me unfortunately).
Thanx & HNY!!!