It is not true. No one gives up any rights by virtue of owning a registered a Title II firearm. A search would come under the same rules as any home search. Of course, owning an unregistered Title II firearn would come under the same rules as possessing any other contraband (illegal drugs, etc.).
I know of no case where BATFE or any other LE agency searched a home solely because the occupant had a registered Title II firearm.
FWIW, I owned a half dozen machineguns/submachineguns for over 40 years and the only contact I ever had with BATFE was to send them a change of address. MD state requires an annual registration, which is a PITA, but other than that, I never heard from the State Police either.
There have been a few cases where police/feds raided a home because of a false report of possession of illegal arms or explosives, the infamous Ballew case being the worst. At one time BATFE "cowboys" seemed to like to raid homes more or less for the fun of it, and on almost any pretext. I believe (or maybe would like to believe) that things have changed. But still I know of no case where registered Title II firearms were involved.