I think that "taking something at face value" has one more meaning. I realized this when my favorite writer wrote a new book and asked her readers to take it at face value.
She used to write in another genre before and her new book was something very different. What she meant by "take it at face value" is that she wanted her readers to look at this new book individually without comparing it to her previous books.
I think this happens a lot with people who come to be known for something specific and do something new and unique suddenly. People might feel disappointed with their new work because they already have preconceived notions about that person's work and have expectations based on that.
So taking something at face value also means that you are going to be open minded and consider that thing individually without comparing it to anything else. Because this is the only way to understand the true worth of something.