I'm not a Geni employee, but the reason pretty much every website does this is so that they have your billing information in case you choose to not cancel the trial. A lot of people accept a free trial but either forget about it or don't care enough to cancel.
On a more practical level, it's also a way of verifying that you actually have the ability to pay should you decide to continue your membership. I think of it as being like a security deposit of sorts.
It's important to note that free membership is available to anyone who wants it on Geni; it's only the Plus and Pro levels that require payment.
I have seen too many free 7 day trials, where you can't quit with less that 2 weeks notice, to feel comfortable by giving my credit card info away.
And it is a pity, as I have many possible tree matches. However, several names in the tree are pretty common, and tree matches like Niels Pedersen ("71 matches in other trees") might be false
If Geni gave a little more info in the teaser and substantiated the match, I would probably buy into merging rights.
Peter, if it makes you feel better, I have profiles with equally common names that have come up as having matches, and I think I've only rejected two or three matches in the past several weeks that I've been able to test this feature. They're not kidding when they say "Smart" Matches; it's remarkably accurate.
Also, from what I've seen, Geni is very, very good about cancellation before the period is up. If you ever have an issue with it, you can let them know and I'm sure they'll be able to help you out.
Obviously, it's up to you to make decisions about whether to upgrade, but it's something to keep in mind if your finances are right for it, now or eventually.
Relating to the quality of the matches, the recent mailings about matches found by Geni do not give any confidence that it is worth the money. Persons that share only first and last names, but have differing middle names, different parents, different spouses, different children, different dates of birth and different countries of birth are presented as matches.