Only a fool would NOT be suspicious of disease crossing the border illegally. Our government can always be trusted to lie about the problems their border policy causes. Disease is one of them, along with bedbugs and other creepy critters.
Diseases crossing our borders would be those that are common in other countries, but not the US. These would be diseases like Chaga's disease, dengue, chikungunya, polio, etc. A disease like EV-D68, which has been extremely rare, is more likely the result of a super-spreader and travel within the US (no foreign involvement necessary).