That's one of those oversimplifications of a general truism.
Ever hear the old saying, "Red sky at night, sailor's delight/Red sky at morning, sailors take warning"? This EQ thing is like that, it's not going to be true 100% of the time, but it indicates a general possibility; just because the sunrise is particularly red does NOT mean it's going to rain, but it often times can indicate an increased *chance* of rain.
The more accurate truism with EQ, which is still only a general guideline and not accurate 100% of the time, but it far better than just the over-simplified "cut don't boost" is , "Use EQ cut to make something sound better/Use EQ boost to make something sound different".
The idea is that if something sounds bad, it's usually because there's too much of something unpleasant in the signal, so you'd remove that by using EQ cut, but if something doesn't sound "bad" per se, but you need to help it cut through or brighten it up a bit more or something like that, that's often done by applying some EQ boost (your 10k boost being a good example of that.)
Of course the implication there - and probably the more important point to remember - is that if something just plain sounds bad, EQ boost may emphasize the "good stuff", but it usually doesn't do much to mask or remove the parts that are making it sound bad; you'll probably still want to remove those with some EQ cut.
There is a correlary EQ truism regarding boost vs' cut. Again, just a general guide, not a scientific rule to be rigidly followed all the time: "Cut narrow/Boost wide".
In other words, usually if your using EQ cut to repair a bad sound, there's a tendency (not always, but on average) for the offending frequencies to be fairly specific or of a fairly narrow bandwidth, so it's often better to surgically remove then with a narrow Q cut rather than a wide "scoop". Conversely, when making something sound sweeter via EQ boost, it's often (on average, but not always) preferable to apply a wider bandwidth "nudge" of just a couple of dB than to create a narrow bandwidth peak.
HTH,
G.