The source makes an important distinction between must stop and may stop.
Prayer must be stopped when an urgently distressed person calls the worshipper for help and the situation genuinely requires rescue.
A parent merely calling — without urgent distress — does not by itself require a person to break a Fard prayer. The commentary gives a separate, more flexible rule for Nafl when a parent does not know the child is praying.
Likewise, if a blind person is very likely to fall into a well or comparable danger, the commentary upgrades intervention from merely permissible to obligatory.