This may be a bit more complex then meets the eye.
While I can't presume to know US Tax Law in this regard - the typical standard with regards to other countries (Canada, UK, etc.) circulates around 'fair market value' and the 'deemed disposition' of property.
Since I'm a Canadian CPA I will highlight using our laws as an example:
If your parents were to 'gift' you the property, they would be absolutely INSANE to do so at a $nil value. We (and the US) assess 'non arms length' (ie family) transactions at fair market value. Irrespective of price - the IRS, CRA, or alternate tax enforcement agency, will want to see your parents dispose of the property at its value, and incur a capital gain. Your 'cost base' would then be this fair market value.
In Canada, if you take the "hide it" approach as suggested, the CRA here will assess your cost base at $nil, and still assess your parents disposition at fair market value. This leads to 'double tax' - an intentional penalty designed into the system. Chances are, if they live in another OECD country, this rule will be in place in some ways shape or form.
In some countries you can perform something called a 'tax deferred roll-over' which would allow your parents to gift their property to a corporation or trust in return for share and debt consideration. For many clients, this is an excellent way to defer capital gains, and also maintain the ability the withdraw funds from the entity on a tax-free basis.
I would highly suggest if this property is significant, you contact a tax lawyer or accountant in the respective country and/or the United States to discuss the most tax efficient manner to transfer the property. There may an upfront cost, but I guarantee this pales in comparison to the interest and penalties you will no doubt be assessed under the discussed 'don't ask, don't tell' model. Based on the limited information here, your Accountant is feeding you some pretty bad advice here. Cash gifts in the United States are limited to certain amounts, so further due diligence is warranted in this regard.
In Canada, these can outpace the value of property in about a year if you receive the maximum penalty, and the Canada Revenue Agency is far less aggressive than the IRS in tax enforcement matters.
Where is the property? It may be an excellent long term opportunity.