It seems that a short comment is not sufficient.
The fact is that there is an r.e. degree which is both cappable and cuppable. The result was proved by Harrington in 1970's in an unpublished handwritten notes. Yang and I have an improvement of this by showing that there is a cappable degree which does not belong to the ideal generated by the union of nonbounding and noncuppable degrees (see https://www.jstor.org/stable/pdf/27588357.pdf?refreqid=excelsior%3Aa9865b098fcf6a982c2dfeeb4155a184).
Certainly you may find earlier published papers that imply the result.