The graph you showed indicates the 95% prediction bounds. The coefficients you provided as a, b, and c have an uncertainty with them that is characterized by the Curve Fitter app. So each parameter needs a confidence bound for where the "true" value is. In short, they're not the same number. If you want to plot the data with prediction bounds like you showed, try doing this.
%Sample Data. Replace x and y with your real data
x = 0:0.1:30;
a = 84.15;
b = 0.1853;
c = 11.8;
y = a./(1+exp(-b*(x-c))) + randi(5,[size(x)]);
%% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( x, y );
% Set up fittype and options.
ft = fittype( 'logistic' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [84.15, 0.1853, 11.8];
prediction_obs = 0.95; %95% prediction interval
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, xData, yData, 'predobs',prediction_obs);
legend( h, 'y vs. x', 'Sigmoid Fit', ...
sprintf('Lower %s%% bounds',num2str(prediction_obs*100)), ...
sprintf('Upper %s%% bounds',num2str(prediction_obs*100)), ...
'Location', 'southeast', 'Interpreter', 'none' );
% Label axes
xlabel( 'x', 'Interpreter', 'none' );
ylabel( 'y', 'Interpreter', 'none' );
grid on
%If you just want the prediction data, use this
ci = predint(fitresult,x,prediction_obs);
