断る doesn't only mean refuse. 前もって断ってください。this sentence means, inform us/me in advance please. so, except for 'refusal', 断り also means 'informing in advance'. 彼は断りもなしに仕事を休んだ。in this sentence, 断りもなしに literally mean 'without asking (permission)', since it's almost the same as saying 'without permission', i think that's why you got confused. although 断り≠許可, but to explain 断りなし, people usually say 'without permission'.

断り≠許可 断り＝拒絶すること

" kotowaru "means "refuse" Does 断り（ことわり）　≠　許可（きょか）

Mr. zigokunokaze is right. 許可=permission normally, 断る=refuse but, '断り' has one more meanings, it is 'asking' , 'getting permission' or 'notice'. For ex. '断りなしに'='without permission' or 'without notice'. '断りなく' is same.