Are we by default leasing our home to domestic helpers?

I have a colleague who was shocked when she saw via real-time recording of her home CCTV that an unidentified man went into her house. That man was led in by her helper (without consent from the employer). That man came into the house when my colleague's 2 years old girl was asleep.
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That man knew his way into the house and which room to go to. He went directly to the helper's bedroom. The thing about real time CCTV is that there is no playback. You can press a record button (when you need to record) but the rest of the footage is not saved (unless you opt for pricier hardware that can accommodate recording for several days before it overwrite).
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Panic struck my friend and she had to leave work to rush home. Several calls were made and neighbour was alerted. My colleague's main concern was for the child. The neighbour was instructed to go into the house and retrieve the baby. Reluctantly, the helper let the neighbour into the house and told the neighbour that she had guest. The guest was let off and most importantly, the baby was safe.
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My friend decided to terminate the helper's contract. The agency advised my friend against reporting to the police because that will delay the replacement. To a family with working parents, my friend had no choice but to comply. The helper was sent home with high probability of returning to Singapore to work. That would be a disaster to the next household.
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After some thoughts, my friend decided to report to the police. After much deliberation, the police decided that there is no case against the helper and the "intruder". The police said that since the helper invited the unidentified man to the house, there is no criminal element to it. My friend insisted that the helper "invited" the man without their consent. To that, the police said that since the helper is staying in my friend's house, she has the right to invite people over.
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All in all, it would suggest that if a household hire a domestic helper, it is by default that the said household is leasing their home to the helper and thus, the helper has the rights to invite people over.
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I was shocked to know this!
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An advice to parents/employers who have to leave their babies at home with domestic helpers (especially without any other family members such as grandparents at home): -
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The next time you renew your helpers' contract, please include a term in the contract that forbids helpers from inviting people over to your houses (esp. without your consent). Having it written in legally binding contract will protect you from having to go through what my friend went through. I guess that would make the "invitation" illegal then.
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For now, the helper is already back to Singapore waiting for the next assignment.
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Just to share.