FYI for what ever its worth.
Our Rav gave a drasha in shul this past shabbos here in Israel.
He said that the shmura matza with the Eida Chareidis Badatz hechsher he bought last year had a bunch of matza kefulos, and some other issues. When he called them up, they said that he had to read their kashrus handbook which said that all the matzos have to be checked, even if they have have their hechsher on it. So he said to not trust a product simply due to the hechser on it.
He also said that he met with a group of them to ask questions, and he asked about relying on the rabbanut hechsher for fruits and veggies. He was told that "Since we are from the Eida Chareidis, we can't tell you that you can rely on their hechsher, even though you are allowed to rely on their hechsher."
(approx quote since I couldn't write it down on shabbos)