Do we need to leave Thailand due to an overstayed visa if my husband's new BOI work permit is approved?

My husband is changing the job from non BOI to a BOI company. Last Thursday he went to cancel his work permit then he went direct to the immigration at chamchuri square but he has been rejected because there were some documents missing and his company ( now his ex company ) couldn't give the documents that day. So he went back to the immigration the next day, and the officer told him that he was over stay already because he cancle already his work permit the day before and the officer told us to leave the country that day and lay the fine.and she told us that she couldn't cancle the visa. After we left the immigration we decided to contacted a person from the BOI company ( the new company that he will work for ) whom take care of our visa and work permit and she told us that we don't need to leave the country because actually our visa and work permit has been approved under BOI a week ago and we actually have 21 day to proceed everything . Is this correct that we don't need to leave the country and won't be fine for over stay ?

I'm sorry for the long story and I hope you guys can understand it. And I hope someone can give me the answer for this situation. Thank you