Use your best judgment. I am not a lawyer, but I suspect that if you use reasonable care to ensure that the creator of the site actually has the rights to license you the images, you don't have to worry about legal concerns. If the site doesn't look shady and says that the textures are original to the site, it's unlikely that you'll get sued.
If you're especially concerned about covering your ass, perform careful documentation. Copy down the license text from the texture site as well as the source URL. If archive.org's Wayback Machine archives the site, you will be able to use it as proof that you acquired the texture in good faith.
As far as attribution goes, it's a good policy in general. Note that the attribution doesn't need to be obtrusive. Unless the content owner specifies a more draconian attribution format, you can just put a note in the credits like "concrete textures from cctextures.blah."