Sorry - this doesn't happen for me. I tested this several times.
Even if I close and re open WD6 and toggle visibility then re publish, the only file re published is the index.xhl (I assume stands for Xara HTML List)
Same if I remove the original export folder and have to export again, no republishing from simply toggling visibility.
This is presumably the file that checks changed site files.
As none are changed by toggling visibility, none are re uploaded.

index.xhl content
Code:
index_htm_files\2.png	372992	3ba343cd45469856160eebe94f2e28b5
index_htm_files\15.png	1013	f0be23fe249d88768b76b63fe70692db
index_htm_files\3.png	983	1e06d781da7088a649883fe1c68c4dc7
index_htm_files\16.png	12565	9dd8cbc41767a4e44a32d080bc8b0b72
index_htm_files\4.png	2349	f44469318590d8152f8ec7eff1c9a2bb
index.htm	11368	71c01c86232c86bf00e8efd43db4c553
index_htm_files\xr_main.css	941	74125aaabdc1607d58aad28ff8f81eb2
index_htm_files\5.png	2352	147554a3f670dd1eccb45a09a5a332dc
index_htm_files\18.png	986	ff194518dab9a227eca4754dcf58ed68
index_htm_files\6.png	6465	903fdc44b835da9ae7b776a010e3da5c
index_htm_files\19.png	11107	869b7478e33f9a8971fbd20e428c4b91
index_htm_files\xr_text.css	1749	81d7951d84bac28a87c6009f3d33c14f
index_htm_files\7.png	108	87754597dccb432da869c31a9db2aceb
index_htm_files\png.js	1194	cdbfd7e64beb89a976e12f8a25b4e1c5
index_htm_files\8.png	110	69c6cdea4bcde5fd20a025b9aef227de
index_htm_files\roe.js	14120	533f2f8907ff52ac7c7a87a8ef8cb490
index_htm_files\9.png	4503	502a039f4010c4c4ef04e88f135e0af4
index_htm_files\0.gif	43	33ea3f4abccdfd74a4a22c5ed55c4731
index_htm_files\20.png	12033	0e32292539369a7b953cf69674edb4d0
index_htm_files\21.png	6080	940c27060867588a4172b52551160bb8
index_htm_files\11.png	7062	1efd749e8f7216df05223b8a96fa7a92
index_htm_files\xr_files.txt	475	963f39116ccead7601862e64fbc60937
index_htm_files\12.png	679	d6e9de719e367847f07ef63fbd588010
index_htm_files\13.png	1000	3ab1bdbed1e92d7e933cc79ce7bbcaea
index_htm_files\0.png	1388	ea7d786fca91956a078243ec7da9c0bc
index_htm_files\14.png	12951	f9eb281d82f5dad12a0cd94e7dcd4d51