N.b. My institution does not have access to this journal and the upload you made has since been deleted
There are a number of ways of scoring the severity of ulcerative colitis on endoscopy; there are at least 8 in clinical use. They all take into account visible features such as vascular patterning, presence of ulcerations, the friability of the mucosal tissue and the presence of mucopurelent exudate.
A nice review of available activity scores in UC is available here:
Elizabeth R. Paine"Colonoscopic evaluation in ulcerative colitis", Gastroenterology Report, Volume 2, Issue 3, 1 August 2014, Pages 161–168, https://doi.org/10.1093/gastro/gou028
Unfortunately, without access to the methods section of this paper it isn't possible for me to say which score and at what threshold they defined "active" and "inactive".
The aim of UC treatment is to induce a remission state, usually through the use of high-dose steroids, then maintain this state with other drugs such as mesalazine. However, the hallmark of UC is "flaring" of the disease where symptoms worsen markedly.
I couldn't find much on the frequency of flares but his paper suggests that ~50% patients self-report a flare once a month or more frequently:
Susan C. Bolge et al.: "Self-reported frequency and severity of disease flares, disease perception, and flare treatments in patients with ulcerative colitis: Results of a national internet-based survey", Clinical Therapeutics, Volume 32, Issue 2, 238-245 https://doi.org/10.1016/j.clinthera.2010.02.010
As others have pointed out, the relationship between disease activity on an endoscopic level and symptom burden for the patient do not necessarily correlate well.