What makes an individual's record "read only"?
Here is the link about read only records. There are some related articles associated with this article.
If you can give us the ID number for the read only record we can look at that and help you determine why it is marked read only. Usually it is a famous person, or a public person.
And I've seen the occasional glitch when a profile is marked Read Only. A few weeks ago, everyone in my direct line was marked read only - even my own profile. The next day, the glitch cleared.