A healthy Chihuahua should not have any problem eating watermelon in moderation. The person asking this question might want to consider their own fruit consumption, though.
When eating too much fruit it is possible for an individual to create issues with calcium storage in the bones, teeth, or brain despite what type of sugar is found within that fruit. Eating less but higher quality fruits can help curtail these types of issues which are what people are referring to when they talk about “the sugar-high problems.” To go further into detail on the subject, the concern arises because high fructose fruits often also contain juices and apple juice concentrate aka high levels of natural sugars/sucrose instead of just glucose…