It's been quite some time since I asked you that. But recently I've been on Atheist Central and thought of you.
It really makes a difference whether or not one has a desire to resolve a question.
You asked why Christians claim outsiders believe in our God but suppress the truth? Well the simplest answer is that the Bible says all people (not just those outside the Christian religion) suppress the truth in unrighteousness (Romans 1:18). From my perspective, the question in your title requires a theological answer. From your perspective, or from others outside my faith, a theological answer may not be expected.
I could explain it like this briefly. We all suppress truth in our minds. That's why we lie, or more obvious, why we often deny our own mistakes or faults. On a larger scale, the evidence is there for us in nature pointing to a supernaturally intelligent Being, but we suppress the knowledge of this Being in our unrighteousness (think denying, lying and taking advantage of others).
That's only the beginning of the theological answer, however. It ends in a message about restoration to righteousness (or uprightness) and peace with our Maker, but not through our own means, rather as a gift from the Creator to the creatures.
I hope you realize I'm only trying to help or at least provide food for thought.
The bible may indeed make the claim. But it is an incorrect claim. Since the bible is wrong (it makes a claim about my state of mind that I know to be incorrect) its unverifiable claims are suspect.
There is dispute over whether the natural world constitues evidence of a supernatural being. But, even if there is a supernatural creator of the universe, it needn't be your god. The bible is already incorrect about my beliefs. It is, therefore, a dubious reference to any gods.
If you are trying to help, you are going about it rather badly. Consider, if I were to insist that you knew your god to be a work of fiction, you would likely pay little heed to anything else I said on the subject. Claiming to know someone else's beliefs pretty much cuts off discussion. (It cuts off discussion with that person, anyway. One might be trying to persuade third parties by demonstrating that stated beliefs are implausible.) If you want to convince me that your god is real and deserving of worship, it is counterproductive to tell me I already believe that but am lying for whatever reason.