Once someone who was writing a halacha book on tefillin for baalei battim asked Rav Eliahsiv if something (I don’t remember what) is a chatzitza. When RE responded that it is not he argued the point. finally RE said “If you want to be machmir be machmir”. The person wrote that RE said that it is good to be machmir.
Someone once asked Rav Mordechai Eliahu about organizing a vacation trip to chutz laAretz. RME said that it is not allowed. He advertised that the trip was with the advice of RME.