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The US Department of State doesn't really do a good job of describing other countries' entry requirements. A better source is the Swiss government itself, which makes no mention of blank passport pages.
Furthermore, the Schengen Borders Code, which discusses stamping of passports, says nothing about blank pages.
The chance of getting a passport stamp in the passport of country A is virtually nil. Far more likely, the officer will put the stamp in the margins of the country B passport, or overlapping other stamps. Image searches show that this practice is quite common.
The safest thing to do in this case is to get a new passport for country B.