matlab-syntax.el:

(matlab--scan-line-for-unterminated-string): When comment found,
disable all quote chars in the comment.
(matlab--scan-line-comment-disable-strings):
Find all syntax " chars and disable as whitespace.

tests/indents.m:
Add tests with ' in comments that impact indent.

matlab-syntax.el

@@ -237,7 +237,9 @@ and `matlab--scan-line-for-unterminated-string' for specific details."
 		(start-char (match-beginning 0)))
 	    (forward-char -1)
 	    (if (looking-at "\\s<")
-		(forward-comment 1)
+		(progn
+		  (matlab--scan-line-comment-disable-strings)
+		  (forward-comment 1))
 	      ;; Else, check for valid string
 	      (if (or (bolp)
 		      (string= start-str "\"")
@@ -267,6 +269,16 @@ and `matlab--scan-line-for-unterminated-string' for specific details."
       (error
        t))))
 
+(defun matlab--scan-line-comment-disable-strings ()
+  "Disable bad string chars syntax from point to eol.
+Called when comments found in `matlab--scan-line-for-unterminated-string'."
+  (save-excursion
+    (while (re-search-forward "\\s\"" nil t)
+      (save-excursion
+	(forward-char -1)
+	(matlab--put-char-category (point) 'matlab--transpose-syntax))
+      )))
+
 (defun matlab--scan-line-bad-blockcomment ()
   "Scan this line for invalid block comment starts."
   (when (and (re-search-forward "%{" (point-at-eol) t) (not (looking-at "\\s-*$")))

tests/indents.m

@@ -170,17 +170,23 @@ function out = array_constant_decls()
 
     % This array has bad syntactic expression parsing due to the
     % apostrophy
-    Closures = [ ...
+    Closures = [ 
         755009 ; ... % 21-Feb-2067 Washington's Birthday (Mon)
-        755010 ; ... % Another row.
+        755010 ;     % !!8
                ];
     
+    dep = [
+        root(info.function, factory, workspace, []), ...    % likewise this isn't a keyword
+        fcn3.finalize                                       % the single quote used to break [] scanning
+          ];
+    
     % !!4
     out = { A     %!!4
             Blong %!!12
             Csep  %!!12
             multinest%!!12
             Closures%!!12
+            dep %!!12
           };      %!!10
 
 end