Nicked Wheel bc of flat tire- ok to use?

[vinuneuro]

Two weeks ago, driving on the highway, one of the tires went flat due to something puncturing it. When the tire guys examined the wheel, there were two nicks/dents, a couple mm deep and maybe 1cm in diameter. One of them is in the middle of the width of the wheel, and the other is on the seam where the wheel bulges up a little. They suggested that the wheel be replaced. Is the integrity of the wheel compromised? I found a single wheel for $200, so if it needs to replaced it's fine...just don't want any wheel cracking/ air losing situations in the future.