I don't just mean that person, I mean anybody who would believe that "I'm a God fearing person" is actually the right thing to say.

I mean, if one thinks about it, it's curious that anybody would openly states that their relation to one's God is "Fear" rather than, say "Love", even if they are being entirely truthful in that.

"God loving" sounds a lot more respectful of a Deity, IMHO.

Further, even for that specific person my point still fits in a twisted way: that person chose that specific expression because deep down they believe people only restrain their bad actions because of fearing retribution.

It's a variant of Psychological Projection and thus still betrays that person's moral makeup: even as non-believers they use the "Fear of God" mantra because they themselves think that claiming that one has one's behavior under constant oversight from a deity which will punish bad behavior is the best way to convince others that one behaves in a good way, and they think so because they themselves restrict their negative behavior towards others through fear of external reprisal rather than through internal mechanisms such as guilt or a personal moral.

Even when people lie, you can still tell a lot about somebody by which lies they think will work best at convincing others.