"A merger always involves capital."
This is definitely not true. A merger CAN ask one company to purchase the stock of another...but it is definitely not required. You are confusing a merger with a buyout or acquisition. In a merger, all that is actually required is for an agreement where two companies decide to work together. This is not recapitalization in ANY way.
You also ignored the rest of the investopedia post where there are many other forms of restructuring that don't require capitalization in any way. Other forms that were listed are:
-change in overall goals
-transfer to a relative
-restructure its financial arrangements
-file for bankruptcy
Let me guess...changing a companies goals REQUIRES capitalization according to you. Because according to the financial experts at investopedia, it is a form of restructuring...and last time I checked, changing a goal or charter does not require additional capital in any way.
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