Heart Rate being normal when under treatment for the bends
You are wrong on several accounts:

Bends occur due to bubbles that form in muscles and joints and not lungs - They fall under Mild or Type 1 Decompression Sickness (Type 1 DCS).
Formation of bubbles in blood stream do occur in the Decompression process - Hyperbaric chamber is used to treat this condition.

What happens when diving:
During deep sea diving the pressure surrounding a person increases at the rate of 1 atm (atmospheric pressure) for every 10 m in sea water and 10.3 m in fresh water. This relation is linear.
The pressure inside the body equalises with the pressure outside to prevent any deformation. The solid and liquid components of the body can withstand pressures upto 151 atm (depth of 1.5 km underwater) without undergoing any noticeable compression. But air, being extremely compressible undergoes compression.
So at 2 atmospheric pressure the space occupied by the air in our body is halved. This would shrink the lungs to half the total volume. To circumvent this the divers breathe air compressed at the same pressure as the water pressure around them, so that the pressure gradient across the chest wall is normal.
Pressure Concentration relationship:

Dalton's Law:
This law states that the Barometric Pressure is the sum of the partial pressures of the individual gases in the air mixture.
Barometric Pressure - The total pressure measured

In air at 1 atmospheric pressure (760 mm Hg) the partial pressures of various gases are:

Nitrogen ~ 593 mm Hg
Oxygen   ~ 159 mm Hg
Co2 ~ 0.2 mm Hg
Others   ~ 7 mm Hg

According to this Law, as the pressure inside the Lungs increase, the partial pressures of each gas increases. At 2 atm, the partial pressures of every gas doubles.
The gas exchange in the lungs is based on partial pressure of the gases. Thus due to increased partial pressure, the amount of gases dissolved in blood increases (This increase is proportionate to the pressure levels).


During a extended dive (one lasting several hours) the body tissues gradually equilibriate with the high-pressure gases. At sea level our body contains 1 L of dissolved nitrogen, equally distributed between body's water and fat. As partial pressure of Nitrogen rises, the nitrogen equilibriates with the body's lipid stores because adipose tissue is relatively underperfused.

Once equilibrium is achieved the volume of nitrogen dissolved in tissues is proportional to the alveolar partial pressure of nitrogen. Thus at 4 atm the body will contain 4 L of nitrogen.
The same principle applies to oxygen as well, though the solubility of oxygen and the speed at which equilibrium is attained are different.
Decompression
During ascent from the depths, the Barometric Pressure (surrounding pressure Pb) falls. As the Pb falls the pressure inside the alveoli fall as well. This causes a fall in the partial pressures of all gases in the lungs creating a gradient of gases from the tissues to the alveoli.
So the diver has to ascend slowly to give enough time for the gases to move into blood from the tissues and then get washed out. If the ascent is too rapid, gases dissolved in the tissues - due to high pressure - attains the gaseous form (due to pressure drop) and become bubbles. This is similar to opening a pressurised coke can where one can observe gas bubbles forming.
The bubbles are the reason for the bends. Bubbles can also cause serious problems like arterial gas embolisation, CNS disorders (due to formation of bubbles in the myelin sheath of axons which compromise nerve conduction), pulmonary symptoms (due to pulmonary emboli), sometimes even Disseminated Intravascular Coagulation.
Solution
The decompression is done in stages - in which the divers spend various amount of time at various under water levels to allow complete diffusion of dissolved gases into blood and into the alveoli which is consequently breathed out.

Hyperbaric Chamber
The hyperbaric chamber is used when the above solution is not applied i.e. the diver has surfaced rapidly without spending sufficient time at various levels to allow proper decompression.
In a hyperbaric chamber the diver is recompressed to the pressures equal to the pressure experienced at the level to which the diver dived. Due to the increase in pressure, the bubbles get dissolved again. This instantly relieves many symptoms - like the nerve conduction delay, bends, niggles etc... Now the decompression is carried out by under controlled environment, simulating the various intervals the diver has to stay at various pressure levels under water.
Hope this explains your doubt.
So coming to myocardial infarction, the hyperbaric chamber redissolves the gas bubbles thus preventing myocardial infarction.

For more info read chapter 61 of Medical Physiology, 2nd edition, by Walter F. Boron and Emile L. Boulpaep.