Yes, that statement is absolutely false. Except for the property taxes (if paid separately or stated separately on your MF bill), none of the MF is deductible, no matter how many timeshares you own. It's a personal expense related to the upkeep of residential property (the timeshare) used for personal purposes, in the same way that utilities, repairs and other upkeep expenditures for your home are not deductible.
An exception would be if you rent your timeshare to others. In that case, all of your expenses related to the timeshare (e.g., property tax, fees, advertising and interest expense - even if on a non-mortgage loan) are deductible to offset the rental income.
For more on the subject of timeshares and income taxes, see the
tax article in the TUG Advice section.