MyHeritage is not "smart" in human terms. It's only a program. It doesn't know that all people born in 1730 are dead. Thus, if the owner of the other tree has not taken off the (default) marker of "alive" when entering the person in question, MyHeritage thinks that this person is still alive, and will display that person's record as "private."
Since you are a member of your own website, you will see all records in your tree displayed. You need to check whether all dead people have a black diagonal line across the upper left corner of the record. If they don't, then MyHeritage considers them still to be alive, and then other people, who are not members of your website, will get them displayed as "private."
I don't know whether you built your tree interactively or whether you are using Family Tree Builder (FTB). FTB offers plausibility checking. You can run diagnostics on your database, and the software will tell you if a person is unreasonably old (like 280 years old and still alive), or if a mother is five years younger than her child.
If you built your tree in MyHeritage, you can export it to Gedcom, then import the Gedcom file to FTB. Then you can run diagnostics on your database, even if your tree was built in MyHeritage.
Hey Jack, reread what the reply said.It matches your question exactly (glad you don't do it).
What I found is that if a person doesn't know the "death" date of a tree person, they DO NOT click the "DECEASED" box so when a smart match is posted, as the reply stated, it is private as the program thinks the tree person is still alive. Maybe a future (near) update to the program may mark anyone born more then 150 years back is automatically marks as deceased.
This is happened to me a lot more than it used to. I supposed it's possible that a majority of people I am matched with have decided recently to make their trees private, but I doubt it. I am starting to think that MH has developed another bug.