The are applies to liars, not to nothing here.
Did you notice that you have but in both your examples? Nothing but as a phrase is used here in an idiomatic sense. We can reread the sentences as:
There are only liars in here.
They are just petty thieves.
That's how it is, I believe.
Edit 2
After your edit, the question becomes one of whether a group of things can be taken as a collective singular, such as in this question, which asks such things as whether a dozen somethings “is” enough.
The answer is that it can be singular if you are thinking of it as one thing as a whole, just as in:
Twelve miles is much too far for me to walk before lunch.
In that sort of sentence, you get agreement like this:
- A few more games is all I have time for.
- A handful of games is all I have time for.
- A few more miles is all I have time for.
- A handful of miles is all I have time for.
It really just depends on what you’re trying to say, and how you’re trying to say it. If you want to say that five matches is more than you can handle or that three olives is too many for a martini, then yes, sure you can.
But normally plural things take plural agreement — see the ngram below, which shows that a handful of men will usually take plural agreement because men is plural, no matter the status of the a handful of premodifer.
It is only when you logically group them as one thing that they take singular agreement. By doing so, that is what you are conveying.
But perhaps your friend does not like it when the council is decided on something, as opposed to when they are divided. :)
Original Answer
Your friend is right, and you are wrong.
When you have a premodifier like a lot of, a number of, or a handful of preceding the head noun, the verb continues to agree with that head noun, instead of with the notionally singular a lot, a number, a handful, which functions more like a red herring than anything else.
Ok, seriously, these premodifiers are really acting like adjectives, not like prepositional phrases. That means the head noun remains the head noun, and there is no change to agreement:
- People think the same way.
- Several people think the same way.
- Few people think the same way.
- No people think the same way.
- Many people think the same way.
- A lot of people think the same way.
- A number of people think the same way.
- A handful of people think the same way.
As opposed to something like:
- If just one out of all those people thinks the same way as you do, you win.
Edit
Although there is a bit of room for variation here, depending on just what the writer is thinking, there is a clear dominance of the plural continuing to be used after a handful of men in this Google N-Gram chart:
Best Answer
The subject of the verb is an invention - which is singular, so the verb-form should be too.
Here are a few written instances of "are an invention that has". Note that Google Books contains no examples of "are an invention that have".
Don't bother even thinking about what Microsoft Word recommends or queries - at best it might be useful for flagging up glaring typos/etc. Beyond that, it has no credibility.