Outside wiring can definitely be an issue. When my RoadRunner service was establishe years ago, they could not make it work until they replaced the coax run from the distribution box to the house. Prior to this the phone company and the cable company took turns in cutting the other's cable. The patches to a cut coax cable were the problem introducing some signal reflections.
In Time Warner Cable's case the modem is theirs. The original was a Motorola CyberSURFR\ufffd Wave modem. This was before the DOCSIS cable modem standards came about. The modem worked for many years. When I started having connection problems, they replaced it with a Toshiba PCX2500 which meets the DOCSIS standard. So far so good.
I was not aware that some cable companies make you buy the modem. Are you paying less than $44.95/mo?