Indeed you're wrong.
A study reported that washing lettuce leaves with tap water for 15 s provided a log reduction of 1.16 (93.08 %) of the E. coli population, while "prolonging washing time with running tap water to 30 s significantly increased (P < 0.05) this reduction to 2.2 log CFU per leaf" — that is, 99.37 %.
The study also mentions better results on cabbage, lemons and tomatoes (though while "thoroughly rubbing" them), and reports that a log reduction of 5.68 (99.9998 %) is achieved after rubbing tomatoes for only 8 s under tap water.
Reference : Reduction of Escherichia coli O157:H7 on Produce by Use of Electrolyzed Water under Simulated Food Service Operation Conditions (open access PDF), Pangloli et al, Journal of Food Protection, 72, 9, 2009. (Note that it uses tap water as control, the purpose of the paper being electrolyzed water.)
NB : You asked about Escherichia coli specifically, but there are similar reports about other pathogens, e.g. another study found that simply rinsing (without rubbing) broccoli/lettuce leaves, apples and tomatoes for 15 s resulted in a removal of Listeria innocua (used as a surrogate for Listeria monocytogenes) by 96.11 %, 99.02 % and 99.21 %, respectively (log reduction of 1.41, 2.01 and 2.10).
Reference : Efficacy of Home Washing Methods in Controlling Surface
Microbial Contamination on Fresh Produce (open access PDF), Agnes Kilonzo-Nthenge, Fur-Chi Chen, Sandria Godwin, Journal of Food Protection, 69, 2, 2006.