You are absolutely correct. It's crucial to exercise caution when providing your credit card details to any platform or service, particularly online. There are some very basic precautions that you need to take, such as checking the SSL and security information, make sure that you trust the payment platform and do not pass the data directly to the site. Even being very careful is easy to fall for scams.
Why not just avoid putting your credit card on website that have not proven to be reliable and go for the trusted and reliable ones, you know they always say free things might purge you meaning you could get scammed to trying to claim those free bonuses that are involved in that particular site you want to link your card. Its better to take precaution that actually getting a result that might destroy you.