However, it is impossible to not lose weight if a person eats below his total daily energy expenditure.

This is true if you either:

• Define "losing weight" such that it includes weight loss due to the decay or cremation of your corpse after death by starvation. Or,
• Observe that if if a body dies rather than burn fat to live then "technically it hasn't expended more energy than was eaten has it? Therefore it doesn't qualify as a counter-example!"

Without such stretching of interpretation, however, it is false, misleading and all too common advice.