(1) I’m not sure how I would have know that.
The only time you would have to pay a house keeper or lawn service is if they are your “Employee”. The only time they would be your “Employee” is if they are not employed by another company offering them as a service and or if they do not qualify as an “Contractor”.
In short the only time they would be an “Employee” is if they are working at your house full time or simply trying to dodge taxes by claiming to be a contractor.
About the only time you “Wouldn’t know” is if they are doing the “Contractor” business and not paying taxes which I would agree get’s really “Dodgy”.
In short the only people that could claim this as a “I didn’t know” would be people that are being lied to. If you have someone working full time at your house, you write them a check directly and not to a company and don’t send them a 1099…you pretty much should know they are your employee.
(2) Can’t understand why its different than any other type of contractor, or self employed person.
See above, it’s not and thus why if you hire a “Contractor” they have very specific rules as to “What is a contractor”. Most people that hire a “Contractor” for a lawn service would not check and may not pay enough to warrant a 1099. OTOH I would think that a “Contractor” that brought their own equipment, worked part time on your lawn and many others could be argued that they are indeed a contractor. But of course the government will come after anyone who will pay the bill 
(3) I would venture to guess that 95% of people that have a house keeper or a lawn service, are “tax cheats” and don’t even know it.
I would agree, but not because of the house keeper or lawn service. If you hire a company that does lawns or cleans houses, you’re not a cheat. If you hire an individual, pay cash under the table…then your a cheat.
That being said I’d guess 95% of everyone inflates their “Charitable giving”, pays someone, baby sitter, handy man, etc cash and neither party reports the transaction. Hell I bet 95% of the people that believe they aren’t “Tax cheaters” are, they just don’t know enough about the tax code to know they are.
Of course I’d bet 95% of people driving a car are in some sort of “violation” as well…I currently have a headlight out 
~Matt