Yes, some can have low back pain.
Tense muscles from anxiety do that.
I think it just depends on where we are weaker in muscle strength that we notice it more, or that area we clench more.
Hope this portion of an article helps.....
One of the tasks stress hormones perform is to cause muscles in the body to contract (tighten). Tight muscles make the body more resilient to attack when in dangerous situations.
Unfortunately, when stress is caused by anxiety (worry, fretting, fearful thinking) and not by a real physical threat where tight muscles may be beneficial for survival, the body still prepares against danger the same way, by causing muscles to tense and tighten, including the muscles in the back. Back pain, tension, and stiffness are all common symptoms of stress- and anxiety-caused muscle tension.