You are correct that this happens. It is infrequent (there are not "many", as you say, compared to true deaths), but it occasionally happens that someone - even in a hospital - is thought to be dead when they are not actually dead. In one of your stories, the girl was presumed to be brain dead, not dead. So strike that one. Hypothermia is a beast all unto itself, and declaring a cold person dead is a bit tricky.*
Determining death is not simple. The International Guidelines for the Determination of Death – Phase I (May 30-31, 2012) Montreal Forum Report is 46 pages long and it still doesn't have a definitive conclusion.
For the most part (and to simplify a bit), death is determined to have occurred when someone is exceedingly unlikely (determined from experience of millions of deaths) to regain function of their heart. It can be from a very wide variety of causes, but basically it follows cardiac arrest or respiratory arrest leading to cardiac arrest.
The procedure is to observe the patient carefully. In hospital, that usually includes electronic monitors of one sort or another. Out of hospital it's by observation. When there is no evidence of cardiac electrical activity capable of generating a pulse, the patient has not been breathing for some time, oxygenation of blood has fallen to beyond critical levels, and there is no neurological activity, they are pronounced dead.**
How do the medical teams or doctors determine then that this person won't all of sudden get a heart beat back?
They "know" because of the combined observations of millions of deaths before that one. Since it has happened, clearly it might happen, but once all the criteria are met, it means they are clinically dead. The exceedingly vast majority of people observed to be clinically dead are, indeed, dead (no possibility to regain function.) There's nothing else to do.
It is roughly estimated from the WHO that about 56 million people die every year. Yet it is not every day that someone who was thought to be dead is not, or it wouldn't make the news. Lets be really generous and say it happens once a month somewhere in the world - 12 times a year - and I think this is very, very generous (there is no known number. I'm guessing it's less in industrialized nations.)
That would mean a death diagnostic accuracy rate of at least 99.9999786% (55,999,988 true deaths in 56,000,000 diagnosed deaths.) That is very, very accurate. It is incredibly difficult and expensive to improve on 99.9999786% of anything for a very small return numerically speaking. It sounds harsh, but it's not. It's what society accepts, including you. If you don't believe me, try to get someone to pass a law changing that.
A better question might be why does this happen? It happens because sometimes a heartbeat is so weak as to be imperceptible to the touch, to sound, and even electronically. The person does not appear to be breathing at all. They have no reflexes to demonstrate neuronal activity (for example, the pupil size doesn't change on shining a light into their eyes.) In the days before burial, that doesn't change 99.9999786% of the time. But if someone's metabolic rate is low enough, they might just survive (being cold increases the chances of this*) and the heart might just start getting stronger and they might just wake up. But the odds of that are so extraordinarily low that the increased expense of storing the body, and checking it again in a more advanced state of decomposition, in addition to the increased risk of contagion... it just doesn't happen, because when someone is declared dead, they are dead 99.9999+% of the time.
The whole situation is frightening to some people. But it's really an irrational fear.
To put the "risk" in more understandable terms - because the difference between life and death are pretty important - in 2013 in the US, there were 16,121 homicides. About 20% of those are stranger on stranger homicides (that is, not domestic violence, gang related, etc.). That means of 316,000,000 people in the US that year, about 3,225 people were killed by someone unknown to them, or one in 97,984. That's much higher than 12 in 56 million (which is roughly one in 4,670,000). Yet, though it's more common, you probably still leave your house most days not worrying that you'll be killed in that year. It's an acceptable risk, though death by firearm at a stranger's hand is never acceptable.
If this is an unacceptable risk to you (I'm not being sarcastic; it is an acceptable risk for me personally), you should stipulate in your will your wishes to be kept in storage and reexamined intermittently over a period of several days longer than usual for signs of life, and include the funds to do this.
*In medicine, we have a saying, "They aren't dead until they're warm and dead." It may seem callous to a reader, but it is precisely to avoid the scenario of which you speak, because someone with a decreased temperature can survive anoxic injury better. In fact, cooling someone down who is in cardiac arrest is not uncommon, and cooling after resuscitation is common.
**Often it is a nurse who discovers someone has died, but in many states, only a doctor, paramedic, or a coroner can declare someone dead. Nurses are often allowed to declare someone dead who is in a nursing home, hospice or a home care patient. Usually (but there is no law) we feel for pulses at various points on the body, we listen for heart sounds with a stethoscope, we listen for breath sounds, we look for chest movement, and I shine a light in the person's eyes looking for a neurological response. If after a few minutes of observation, nothing has been found, the patient is then pronounced.
The International Guidelines for the Determination of Death – Phase I May 30-31, 2012 Montreal Forum Report available in full online in PDF
"I Pronounce This Patient Dead" shows that it's not easy even for doctors
Cooling the body after resuscitation following cardiac arrest
All homicides CDC