There's a real-life basis for that:
mosquitos trapped in amber can remain intact for millions of years.
It is plausible for an insect with intact DNA to be thus recovered from up to the late Jurassic.
DNA in exposed bones decays too fast (a few million years at most) to be recovered from a dinosaur fossil.
In real life, there have been plausible but eventually disproven reports of dinosaur DNA findings .
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Bones turned into fossils cease being bone; fossilization is the slow process of replacing biological matter with deposited minerals, but retaining the shape of the bones.
Few fossils actually have any biological proteins left, let alone the obnoxiously fragile DNA.
Critters preserved in amber, however, are protected in a closed organic polymer container, in an anaerobic state, and have little, if any, chemical replacement.
The mosquito's DNA is readily obtained; the meal, less so, as the insect's own digestive system contains chemicals which break down blood.
Even so, it's still often fragmented due to age.
Some DNA from blood in mosquitos has been sequenced, but I recall it not being able to be identified as to source.
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I think the whole point is something like "quality rather than quantity".
As I understand it correctly the reason they are using DNA from mosquito is because it is in amber.
Therefore it is said that the DNA is well (fully) preserved.
On the other hand because a bone would be exposed to outside elements it should be fragmented.
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I think the concept is that the insects trapped in amber are essentially unchanged as they are completely sealed off.
From what I've heard though, the DNA still deteriorates, and the oldest viable DNA that's ever been recovered is less than 100K years old.
So no hope for dinosaur DNA.
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Fossils aren't bones.
They're rock, there's little if any DNA because a fossil of a bone has been virtually mineralized into a rock.
There's no DNA to obtain.
Even if a mosquito with dino blood in it's gut was preserved in amber, at geologic burial underground temps are ambient as much as 58 degrees Fahrenheit, not ideal preservation temps.
The DNA is at least 65 million years old, so given it's composition (DNA is made of sugar and phosphates)
it would biodegrade over time.
PLUS mosquitoes have nuceloese enzymes in their gut to break down blood for digestion.
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In Jurassic park, Dinosaurs are resurrected by DNA stored in mosquitoes, who had sucked dinosaur blood. Is there any particular reason why more DNA would be stored in a mosquito than in a bone or similar device?
Would more DNA be stored in mosquitoes than bones?
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Mosquitos trapped in  amber  can remain intact for millions of years, as they are protected in a closed organic polymer container, in an anaerobic state, and have little chemical replacement. Therefore, it is plausible for an  insect  with intact DNA to be recovered from the late Jurassic period.  It is said that some DNA from blood in mosquitos has been sequenced, but the source of that blood was not identified. Conversely, DNA in exposed bones  decays too fast (a few million years at most) to be recovered from a dinosaur fossil. There is a better chance of finding DNA in a mosquito trapped in amber than in bones. This is because the amber acts as a seal and preserves the DNA whereas DNA in exposed bones decays fast.
DNA trapped in amber is better preserved because the amber acts as a seal. Therefore the chances of finding DNA are qualitatively higher. DNA in exposed bones decays too fast.