"They wouldn't do that, would they?" this describes how the caps are fitted into the board
Badcaps.net - Cap Removal They do connect to various layers but it seems as long as you have solder IN the hole - no gaps - you should be OK. Also read the link you posted yourself above re the fitting
Re the board labelling see this
Badcaps.net - Cap Installation Don't forget your board is made by Asus
".....If you look at the marking on the motherboard where the old capacitor once resided, you will notice a 'half moon' white shaded area there. The lead that is in that white area represents the NEGATIVE pole of the capacitor. On the actual capacitor, the negative side is clearly marked with a 'minus' sign running down the NEGATIVE side. ..........
This does not always hold true on all motherboards!
Some boards, especially most Asus boards, are reverse marked on the silkscreens, the 'half moon' area is actually the POSITIVE pole!! Pay attention to the markings on the board AND the markings on the original caps as you remove them!! As a rule though, the white shaded area represents the NEGATIVE pole, just make sure you check yours as you remove the old caps!"
and from
Capacitor Lab - Types of Capacitors - Radial Electrolytic Capacitors
"Not all PCBs follow this rule though. ASUS actually uses the white shaded part to indicate the positive lead on their PCBs, which is quite confusing."
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For interest, theres a dedicated bad caps forum at
Badcaps Forums - Salvation For Your Hardware!
and heres another long forum thread on the topic of bad caps in PCs
The Mother Board :: View topic - Bad bad capacitors