A center stripe is almost certainly an indication of a solid wood back, but lack of a center stripe doesn't necessarily indicate a laminated back. It depends a lot on what wood the guitar's made from. Mahogany is readily available in wide enough widths to make one-piece backs. (Martin's 15 series guitars are all solid mahogany and they have one-piece backs.) But rosewood in that sort of width would be prohibitively expensive.

Also, and this should go without saying, if the back has no braces, it's a 100% guarantee it's laminated. Braces aren't really needed on laminated backs. My Guild 12-string has a laminated maple back and there's not a brace in sight.