There is strong evidence suggesting the Qin legal system did not cause revolts in the rest of China. The story, as told by the Sima Qian in Shiji, says that the first rebels rebelled because, supposedly, they were conscripted for military services, but were delayed by a rainstorm. As the punishment for being late was death, they rebelled.

Sima Qian and Han dynasty records had a vested interested in vilifying the Qin, the regime they overthrew. This, among many other claims is immediately suspect. First, according to the Shiji, Chen Sheng, chosen chief to lead this group of conscripts, told them :

皆已失期，失期當斬。藉弟令毋斬，而戍死者固十六七。
We're all already late, for being late we shall be executed. If you manage not to be executed, six or seven in ten of you will die in garrison duty.

Chen Sheng (or Sima Qian) here is clearly contradicting himself. Clearly they would not all be executed if there were going to be enough survivors for 60% to 70% to then die on garrison duty. How would they know the expected casualty-rate anyway? Archeological finds also calls such an assertion into question. According to legal codes found in a 217 BC tomb, the punishment for tardiness for labour conscripts were a reprimand for three to five days late, a fine of one shield for six to ten days, a fine of one armor for over ten days. These fines were exacted on the official organizing the conscripts, not the group leader (like Chen Sheng) selected from the conscripts to lead subgroups during travel. Not only that, an exception to the law was made in case of delay caused by heavy rain, which was precisely the (supposed) case for Chen Sheng's 209 BC rebellion. While the law was for labour conscripts, not military, given the way it was set out (no executions, different punishments based on severity, punishment exacted only on the leader responsible, and reasonable exceptions allowed) it is highly unlikely Chen Sheng or any of his 900 group of military conscripts would have been executed. If Sima Qian (or his source) didn't make this up, then most likely Chen Sheng did to trick the rest of the men into supporting his rebellion. Note that in context just before Chen Sheng told the men this, he and his buddy Wu Guang had just killed the officers presumably commanding their group.

With this story being highly unlikely, others become equally suspect as well. Traditionally the Qin system was blamed for being highly demanding on the society, greatly overburdening the poor. This, however, is also highly questionable. One basis for this is, when talking about Chen Sheng's group, Shiji and other Han Dynasty sources say a force of nine hundred men was conscripted from "the left side of the village" which has traditionally gave rise to two different explanations. One is that the poor or otherwise exempt lived on the "left" and so were not supposed to serve. Another is that all the people on the "right" were already called up. Both suggest a massive, excessive conscription effort that bled the labour force dry. However, there's no reason to think these interpretations are correct. Indeed, the latter suggesting conscripting half of all able-bodied male is simply not possible in an agrarian society. There's really no reason to think these are the correct interpretation of Han records, or that the Han records interpreted Qin conscription correctly. The next sentence says:

陳勝、吳廣皆次當行
Chen Sheng and Wu Guang were among those whose turn it was to go...

In other words, it was simply an alternating system. And there's no reason why it was just "left and right" and not "left, right, upper, lower". Even if it was just "left and right", the passage also opens up the possibility that there was further selection on those who lived on the "left". There's also nothing to suggest "left" meant the exempt or poor who would've been overly burdened.

A related charge is that the Qin conscripted too much labour for construction of Afang Palace and the First Emperor's Tomb. However, close examination of the Shiji passages show that the labours used were convicts, not conscripts. When 30,000 families were moved to the tomb town and 50,000 families moved to the terminus of one of Qin's new highways, the families were exempt from conscript labour for ten years. Both of these seems very reasonable, or at least not nearly as harsh as usually accused of the Qin.

Next, let's look at taxes. The Huainanzi and Hanshu accused the Qin of collecting "the greater half" (meaning two thirds) in taxes. This is simply impossible, as there's little to suggest agricultural productivity was so high that farmers could subsist on only a third of the harvest. Han Dynasty Confucian scholar Dong Zhongshu also tell us at the time landless peasants paid 50% of their produce as rent to landlord. Dong Zhongshu himself is known for wild exaggerations. If the exaggerated rent payment is 50%, and the tax, presumable paid by the landlord, is 66%, who would want to be a landlord? Examination of passages in the Shiji shows the Qin collected a poll tax per family plus an agricultural tax. While we don't know the exact tax rate of each, having two separate taxes in reality suggest the two-thirds figure in other Han dynasty sources are a hand-waved propaganda, and they never actually sat down to calculate the tax rate.

Similarly, this passage of the Shiji:

當食者多，度不足，下調郡縣轉輸菽粟芻稿，皆令自齎糧食，咸陽三百里內不得食其穀。

Is often interpreted similar to the following:

As there were many mouths to feed in the capital and not enough provisions, grain and fodder were levied from the provinces, transport workers were ordered to supply their own rations, and all grain within three hundred li of Xianyang was commandeered.

How exactly could a government put a 100% tax rate, basically a death sentence, without immediate widespread revolt, which was not noted.

A more accurate translation would be:

...The commanderies and prefectures in transporting...were all ordered to provide their own rations. Within three hundred li of Xianyang, [they, i.e., those who transported grain] were not permitted to eat their grain [that they were transporting].

In other words, to solve this temporary shortage, workers transporting food to the capital were ordered to bring their own rations instead of eating from the food they were transporting. A bit of a (temporary) burden for sure, but not unreasonable and certainly not condemning anyone to death.

The final nail in the coffin, is the Shiji's record of Chen Sheng and Wu Guang discussing rebellion. Cheng Sheng says:

天下苦秦久矣。吾聞二世少子也，不當立，當立者乃公子扶蘇。扶蘇以數諫故，上使外將兵。今或聞無罪，二世殺之。百姓多聞其賢，未知其死也。項燕為楚將，數有功，愛士卒，楚人憐之。或以為死，或以為亡。今誠以吾眾詐自稱公子扶蘇、項燕，為天下唱，宜多應者。
The world has long suffered under the Qin. I have heard that the Second Emperor is a younger son and ought not to have ascended the throne. The one who ought to have ascended the throne is Prince Fusu. Because Fusu had repeatedly admonished the former emperor, the former emperor had sent him out to command armies. Now some have heard that though he was without crime, the Second Emperor has killed him. Many of the commoners have heard that he is worthy but they do not know that he is dead. Xiang Yen is a Chu general who repeated earned merit and who was kind to his troops. The people of Chu have a tender regard for him. Some think that he has died; some that he has fled. Now certainly, using our group, if we falsely call ourselves Prince Fusu and Xiang Yen and issue a call to the world, many will respond.

If the Qin was so unpopular, why would the rebels pretend to be important members of the regime (a general and the original heir to the throne) to rally support to their cause. The logical conclusion is that the Qin was not unpopular. The Second Emperor and his government was. And indeed, most of the early Han sources pin the Qin's fall on Zhao Gao and Li Si. The First Emperor wanted to have Fusu succeed (and logically placed him with the army), but after his death the two of them fabricated his decree to have Fusu and the general Meng Tian commit suicide. Zhao Gao then had Li Si executed and the government then went to hell.

In short, a succession crisis and a bunch of scheming men caused the political instability that brought down the Qin. The Qin legal system itself was not to blame.

Source: Dull, J. (1983). Anti-Qin Rebels: No Peasant Leaders Here. Modern China, 9(3), 285-318.