I don't think this is fixable, at least not within Basic4ppc. What happens is that the Table gets itself in a state where it has drawn itself with the column headers visible but the HeaderVisible property returns False. Trying to set the HeaderVisible again to False does not cause the Table to redraw, possibly because it sees no need to as it knows the headers are not visible. Setting HeaderVisible to True then immediately False sorts it out and it redraws. The attached demo shows this.
As A Table is a compound control it seems that some bits of it get out of sync. I think this happens if you set the HeaderVisible property before the Table has been fully built or drawn and only seems to happen when the Table is added before the Form is shown. Tables created in the Designer work OK.