I previously added my comment about "don't forget the improvement costs" and was going to end there.

Maybe because I accidentally "killed" the mother (at the time of "the gift"), or perhaps 10/24 and two to the power 10 both meant something to me - but then also maybe I'm in denial of being very behind for the 10/15 drop dead date - I'm pouring out my mind as follows. 

You said: The resulting transaction was that one parent would still have ownership of 50% and the three kids would have a 1/6 interest in the property.  Fast forward twenty years, the remaining parent (with 50% interest) have now passed on and with skyrocketing home values, children have all decided to sell the property at a significant gain. 

So, FORM: Sibling A owns 2/3; Sibling B and C: 1/6 each.    (Your client is B or C or both, but NOT A)

Substance: ???

There were a few pieces of facts that could make substance different from FORM.  Examples:

*  Did A pay the 50% original cost and the annual costs?  If NOT what was Mother's and the family's intent/understanding?

*  Who paid for the cost / improvements over the years.  (IF mother put in significant improvements, should the improvement costs basis be split 1/3???)   IF mother paid the property taxes over they years, any way to equalize???

*  Did mother stay in the house?  Was it relevant, as I inferred from the point by @BobKamman ? 

* .....

Now, if you were to take Substance over FORM, you would need to first make sure it had reasonable basis to support the position for taking Substance.  The tax authority at time would take the best position for the government and disagree with TP's treatments.  In many cases, to protect the government 's interest, when TP takes form, the government takes substance, and vice versa.  Thus, it could be tricky and all factors should be considered.

Even if TP could the position of Substance over FORM, or whatever, the key question I would ask my client in a case similar to this is:

What did the siblings agree on?

We could sit here and analyze the case to kingdom come, but if there is an argument/fight by the siblings, it could put your conclusion or tax recommendation in a very awkward position.  My experience is that when it comes to money, inheritance... etc., even siblings otherwise in good terms could turn on each other.  If they were still very amicable, there would always be that one spouse who would do the wedge-driving thingie.  Before my client gives me a clear indication of what the siblings have agreed on, in writing (email communication comes in handy in this), I would NOT finalize the tax position, as it could be part of the bone of disagreement or even litigation down the road.

Remember, the tax positions for A B and C would also imply their ownership of the funds from the sale.  Also, their tax positions should be consistent.  For the love of harmony, I wish they are in total agreement in the deal. 

I always let the client decide how to treat the SUBSTANCE.  Once that is done and if the Substance has substance, applying the tax law should be a breeze.  

For me to look at the facts - even if I had all the facts, let alone the facts in this case were presented piecemeal and partially - and decide on the tax treatment, without getting the clear understanding of the clear understanding among the THREE siblings, it could  just be my sheer arrogance.  

Perhaps I sound cynical, but this is from my years of dealing with families, especially with inherited properties, and also from the weekend bourbon that has not gone away from my system.

Hope I'm not infringing too much.  Or too cynical.

I wish you the best.