You probably have the setting enabled that automatically determines the sheet scale when a part is inserted. You can find it in the Options > Drawings section. There is no need to disable it because using the sheet scale as the scale for your views is proper practice.
When the boxes are drawn on the sheet instead of in the sheet format, they might get scaled together with your views. I think that is what is happening here. If you right click the drawing area and select Edit Sheet Format, do the boxes appear or not? You should move them into your sheet format if they should be present at any drawing. Otherwise you may want to save them as blocks and insert them when necessary.
There is also a pop-up question that asks you if you want to scale annotations when the sheet scale changes. You might have disabled that pop-up. You can check those ignored messages in the last tab of the options menu.
Thanks for the input--deselecting the part automatically determining the sheet scale works. One simply has to change the scale of the part/assembly view afterwards and this has no ill-effect upon the text and lines.
I find it problematic to place certain things aside from title block and borders on the Sheet Format as everything on the Sheet disappears and things invariably overlap as one has to try and remember where drawings views, notes &c&c were and "eyeball" and hope for no overlaps which can be painstaking to align.
I'll also look into the pop-up regarding scaling annotations.