Yes. Unquestionably.
Here are a few different articles from around the gulf coast states that speak to this:
https://www.khou.com/article/news/health/coronavirus/houston...
https://www.npr.org/2021/08/19/1029260134/alabama-hospitals-...
Something that may be a little confusing as well is what does "full" mean. Both morally and legally, it is very difficult for a hospital to turn someone away. Rather than turn someone away, the hospital will have new people wait, attempt to make more room, and provide less care to more people. This leads to the question: Is a hospital full if they're stashing patients in hallways and providing hallway care? Within an ICU, typical care is either one nurse to two patients or one to one depending on the reason for the ICU stay. At the moment, the ratios are 3-4 to 1, which is not the standard of care, but the best they can do. Does this count as a hospital being full?
On a more personal note, my wife is an ICU physician. At the moment, I'm writing this from a hotel room because I started traveling with her to help alleviate the stress from her work. On this trip, she will do seven days of twelve hour shifts in a row. The hospital has asked us to stay for longer, but we're exhausted and have work elsewhere. This sort of thing does not happen during flu season, so I will assert strongly that we are still not close to the realm of normal.
In a direct answer to your manpower question, this hospital does not have enough staff. They don't have enough physicians and they don't have enough nurses. Recently, this particular hospital acquired multiple new ECMO units, which do absolutely help with care. They can't use them. They don't have the nurses.
As one more anecdote, a friend of my wife who is also an ICU physician called the other day with a story from her unit. She just admitted a patient who spent six days waiting in the ER with COVID. They had no available, staffed beds until then.
Now, to be sure, I am just another voice on the internet. You can choose to believe me or not and that's fine. I will say that getting news from what actually occurs in the hospital is difficult. Reporters are people too and they're not necessarily trained to understand the nuance of hospital reality. That doesn't mean what they report isn't useful, but it may be frustratingly incomplete.
Some questions that may help with any personal investigation:
1. What are the number of staffed bed available in the hospital? Beds are different than staffed beds, but they are sometimes used synonymously. Right now, with the lack of staff, it may not be.
2. Are the ICUs in the Level 1, 2, or 3 trauma centers full? Trauma center designation gives information about the number and type of staff that a hospital is required to keep available 24-hours a day. Generally speaking, the large trauma centers have better staff and better equipment. Even if there is an ICU bed available in a regional medical center, it doesn't mean it can provide the care required. Simply, they may not have the equipment or specialists required for care. As long as the large hospitals in the cities are full then transfer is not possible and overall medical care in that region is reduced.