Yes, re: the BSL4, according to Wikipedia:

"Biosafety level 4

This level is required for work with dangerous and exotic agents that pose a high individual risk of aerosol-transmitted laboratory infections, agents which cause severe to fatal disease in humans for which vaccines or other treatments are not available, such as Bolivian and Argentine hemorrhagic fevers, Marburg virus, Ebola virus, Lassa virus, Crimean-Congo hemorrhagic fever, and various other hemorrhagic diseases. This level is also used for work with agents such as smallpox that are considered dangerous enough to require the additional safety measures, regardless of vaccination availability. When dealing with biological hazards at this level the use of a positive pressure personnel suit, with a segregated air supply is mandatory. The entrance and exit of a level four biolab will contain multiple showers, a vacuum room, an ultraviolet light room, and other safety precautions designed to destroy all traces of the biohazard. Multiple airlocks are employed and are electronically secured to prevent both doors from opening at the same time. All air and water service going to and coming from a biosafety level 4 (or P4) lab will undergo similar decontamination procedures to eliminate the possibility of an accidental release.

Agents with a close or identical antigenic relationship to biosafety level 4 agents are handled at this level until sufficient data are obtained either to confirm continued work at this level, or to work with them at a lower level.

Members of the laboratory staff have specific and thorough training in handling extremely hazardous infectious agents and they understand the primary and secondary containment functions of the standard and special practices, the containment equipment, and the laboratory design characteristics. They are supervised by qualified scientists who are trained and experienced in working with these agents. Access to the laboratory is strictly controlled by the laboratory director.

The facility is either in a separate building or in a controlled area within a building, which is completely isolated from all other areas of the building. A specific facility operations manual is prepared or adopted. Building protocols for preventing contamination often use negatively pressurized facilities, which, even if compromised, would severely inhibit an outbreak of aerosol pathogens.

Within work areas of the facility, all activities are confined to Class III biological safety cabinets, or Class II biological safety cabinets used with one-piece positive pressure personnel suits ventilated by a life support system."

https://en.wikipedia.org/wiki/Biosafety_level

I don't think that poor nurse in Dallas was at all prepared. She obviously didn't have what she needed to keep from being infected.